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Journal articles on the topic 'Orbifold cohomology'

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Author: Grafiati

Published: 14 March 2023

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1

Pronk, Dorette, and Laura Scull. "Translation Groupoids and Orbifold Cohomology." Canadian Journal of Mathematics 62, no. 3 (June 1, 2010): 614–45. http://dx.doi.org/10.4153/cjm-2010-024-1.

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AbstractWe show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps, giving a mechanism for transferring results from equivariant homotopy theory to the orbifold category. As an application, we use this result to define orbifold versions of a couple of equivariant cohomology theories: K-theory and Bredon cohomology for certain coefficient diagrams.

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2

PFLAUM, M. J., H. B. POSTHUMA, X. TANG, and H. H. TSENG. "ORBIFOLD CUP PRODUCTS AND RING STRUCTURES ON HOCHSCHILD COHOMOLOGIES." Communications in Contemporary Mathematics 13, no. 01 (February 2011): 123–82. http://dx.doi.org/10.1142/s0219199711004142.

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In this paper, we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case, the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an S1-equivariant version of the Chen–Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology.

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3

GOLDIN, REBECCA F., and MEGUMI HARADA. "ORBIFOLD COHOMOLOGY OF HYPERTORIC VARIETIES." International Journal of Mathematics 19, no. 08 (September 2008): 927–56. http://dx.doi.org/10.1142/s0129167x08004947.

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Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients T*ℂn//// T of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the combinatorics of hyperplane arrangements. By developing hyperkähler analogues of symplectic techniques developed by Goldin, Holm, and Knutson, we give an explicit combinatorial description of the Chen–Ruan orbifold cohomology of an orbifold hypertoric variety in terms of the combinatorial data of a rational cooriented weighted hyperplane arrangement [Formula: see text]. We detail several explicit examples, including some computations of orbifold Betti numbers (and Euler characteristics).

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4

Goldin, Rebecca, Megumi Harada, Tara S. Holm, and Takashi Kimura. "The full orbifold K-theory of abelian symplectic quotients." Journal of K-Theory 8, no. 2 (June 10, 2010): 339–62. http://dx.doi.org/10.1017/is010005021jkt118.

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AbstractIn their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifoldK-theory of an orbifold , analogous to the Chen-Ruan orbifold cohomology of in that it uses the obstruction bundle as a quantum correction to the multiplicative structure. We give an explicit algorithm for the computation of this orbifold invariant in the case when arises as an abelian symplectic quotient. To this end, we introduce the inertial K-theory associated to a T -action on a stably complex manifold M, where T is a compact abelian Lie group. Our methods are integral K-theoretic analogues of those used in the orbifold cohomology case by Goldin, Holm, and Knutson in 2005. We rely on the K-theoretic Kirwan surjectivity methods developed by Harada and Landweber. As a worked class of examples, we compute the full orbifold K-theory of weighted projective spaces that occur as a symplectic quotient of a complex affine space by a circle. Our computations hold over the integers, and in the particular case of these weighted projective spaces, we show that the associated invariant is torsion-free.

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5

Bahri, Anthony, Soumen Sarkar, and Jongbaek Song. "Infinite families of equivariantly formal toric orbifolds." Forum Mathematicum 31, no. 2 (March 1, 2019): 283–301. http://dx.doi.org/10.1515/forum-2018-0019.

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AbstractThe simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed integrally equivariantly formal. In all cases, it is possible to give a description of the cohomology ring and to relate it to the cohomology of the original orbifold.

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6

BAK, L., and A. CZARNECKI. "A REMARK ON THE BRYLINSKI CONJECTURE FOR ORBIFOLDS." Journal of the Australian Mathematical Society 91, no. 1 (August 2011): 1–12. http://dx.doi.org/10.1017/s1446788711001455.

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AbstractThe paper presents a proof of the Brylinski conjecture for compact Kähler orbifolds. The result is a corollary of the foliated version of the Mathieu theorem on symplectic harmonic representations of de Rham cohomology classes. The proofs are based on the idea of representing an orbifold as the leaf space of a Riemannian foliation and on the correspondence between foliated and holonomy invariant objects for foliated manifolds.

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7

Baranovsky, Vladimir. "Orbifold Cohomology as Periodic Cyclic Homology." International Journal of Mathematics 14, no. 08 (October 2003): 791–812. http://dx.doi.org/10.1142/s0129167x03001946.

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It is known from the work of Feigin–Tsygan, Weibel and Keller that the cohomology groups of a smooth complex variety X can be recovered from (roughly speaking) its derived category of coherent sheaves. In this paper we show that for a finite group G acting on X the same procedure applied to G-equivariant sheaves gives the orbifold cohomology of X/G. As an application, in some cases we are able to obtain simple proofs of an additive isomorphism between the orbifold cohomology of X/G and the usual cohomology of its crepant resolution (the equality of Euler and Hodge numbers was obtained earlier by various authors). We also state some conjectures on the product structures, as well as the singular case; and a connection with a recent work by Kawamata.

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8

Hepworth, Richard. "Morse inequalities for orbifold cohomology." Algebraic & Geometric Topology 9, no. 2 (June 2, 2009): 1105–75. http://dx.doi.org/10.2140/agt.2009.9.1105.

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9

Fernandez, Javier. "Hodge structures for orbifold cohomology." Proceedings of the American Mathematical Society 134, no. 9 (February 17, 2006): 2511–20. http://dx.doi.org/10.1090/s0002-9939-06-08515-7.

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10

Pagani, Nicola. "Harer stability and orbifold cohomology." Pacific Journal of Mathematics 267, no. 2 (May 11, 2014): 465–77. http://dx.doi.org/10.2140/pjm.2014.267.465.

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11

G�ttsche, Lothar, and Barbara Fantechi. "Orbifold cohomology for global quotients." Duke Mathematical Journal 117, no. 2 (April 2003): 197–227. http://dx.doi.org/10.1215/s0012-7094-03-11721-4.

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12

Goldin, Rebecca, Tara S. Holm, and Allen Knutson. "Orbifold cohomology of torus quotients." Duke Mathematical Journal 139, no. 1 (July 2007): 89–139. http://dx.doi.org/10.1215/s0012-7094-07-13912-7.

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13

Adem, Alejandro, Ali Nabi Duman, and José Manuel Gómez. "Cohomology of toroidal orbifold quotients." Journal of Algebra 344, no. 1 (October 2011): 114–36. http://dx.doi.org/10.1016/j.jalgebra.2011.08.004.

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14

Pan, JianZhong, YongBin Ruan, and XiaoQin Yin. "Gerbes and twisted orbifold quantum cohomology." Science in China Series A: Mathematics 51, no. 6 (June 2008): 995–1016. http://dx.doi.org/10.1007/s11425-007-0154-9.

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15

Chen, Weimin, and Yongbin Ruan. "A New Cohomology Theory of Orbifold." Communications in Mathematical Physics 248, no. 1 (May 4, 2004): 1–31. http://dx.doi.org/10.1007/s00220-004-1089-4.

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16

Pronk, Dorette, and Laura Scull. "Erratum: Translation Groupoids and Orbifold Cohomology." Canadian Journal of Mathematics 69, no. 4 (August 1, 2017): 851–53. http://dx.doi.org/10.4153/cjm-2017-004-3.

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17

Ruan, Yongbin. "Discrete Torsion and Twisted Orbifold Cohomology." Journal of Symplectic Geometry 2, no. 1 (2004): 1–24. http://dx.doi.org/10.4310/jsg.2004.v2.n1.a1.

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18

Uribe, Bernardo. "Orbifold Cohomology of the Symmetric Product." Communications in Analysis and Geometry 13, no. 1 (2005): 113–28. http://dx.doi.org/10.4310/cag.2005.v13.n1.a3.

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19

Stapledon, A. "Weighted Ehrhart theory and orbifold cohomology." Advances in Mathematics 219, no. 1 (September 2008): 63–88. http://dx.doi.org/10.1016/j.aim.2008.04.010.

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20

Yasuda, Takehiko. "Twisted jets, motivic measures and orbifold cohomology." Compositio Mathematica 140, no. 02 (March 2004): 396–422. http://dx.doi.org/10.1112/s0010437x03000368.

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21

Mann, Etienne. "Orbifold quantum cohomology of weighted projective spaces." Journal of Algebraic Geometry 17, no. 1 (January 1, 2008): 137–66. http://dx.doi.org/10.1090/s1056-3911-07-00465-1.

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22

Zaslow, Eric. "Topological orbifold models and quantum cohomology rings." Communications in Mathematical Physics 156, no. 2 (September 1993): 301–31. http://dx.doi.org/10.1007/bf02098485.

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23

Du, Chengyong, and Tiyao Li. "Chen-Ruan Cohomology and Stringy Orbifold K-Theory for Stable Almost Complex Orbifolds." Chinese Annals of Mathematics, Series B 41, no. 5 (September 2020): 741–60. http://dx.doi.org/10.1007/s11401-020-0231-8.

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24

Jiang, Yunfeng. "The Chen–Ruan Cohomology of Weighted Projective Spaces." Canadian Journal of Mathematics 59, no. 5 (October 1, 2007): 981–1007. http://dx.doi.org/10.4153/cjm-2007-042-6.

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AbstractIn this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen–Ruan cohomology ring of weighted projective space

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25

Dijkgraaf, R., V. Pasquier, and P. Roche. "Quasi hope algebras, group cohomology and orbifold models." Nuclear Physics B - Proceedings Supplements 18, no. 2 (January 1991): 60–72. http://dx.doi.org/10.1016/0920-5632(91)90123-v.

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26

Jiang, Yunfeng, Hsian-Hua Tseng, and Fenglong You. "The quantum orbifold cohomology of toric stack bundles." Letters in Mathematical Physics 107, no. 3 (November 15, 2016): 439–65. http://dx.doi.org/10.1007/s11005-016-0903-1.

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27

Coates, Tom, Alessio Corti, Yuan-Pin Lee, and Hsian-Hua Tseng. "The quantum orbifold cohomology of weighted projective spaces." Acta Mathematica 202, no. 2 (2009): 139–93. http://dx.doi.org/10.1007/s11511-009-0035-x.

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28

Coates, Tom, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng. "A mirror theorem for toric stacks." Compositio Mathematica 151, no. 10 (June 1, 2015): 1878–912. http://dx.doi.org/10.1112/s0010437x15007356.

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We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks${\mathcal{X}}$. This determines the genus-zero Gromov–Witten invariants of${\mathcal{X}}$in terms of an explicit hypergeometric function, called the$I$-function, that takes values in the Chen–Ruan orbifold cohomology of${\mathcal{X}}$.

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29

Jiang, Yunfeng. "The orbifold cohomology ring of simplicial toric stack bundles." Illinois Journal of Mathematics 52, no. 2 (2008): 493–514. http://dx.doi.org/10.1215/ijm/1248355346.

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30

Negron, Cris, and Travis Schedler. "The Hochschild cohomology ring of a global quotient orbifold." Advances in Mathematics 364 (April 2020): 106978. http://dx.doi.org/10.1016/j.aim.2020.106978.

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31

Pagani, N., and O. Tommasi. "The orbifold cohomology of moduli of genus 3 curves." Manuscripta Mathematica 142, no. 3-4 (February 2, 2013): 409–37. http://dx.doi.org/10.1007/s00229-013-0608-z.

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32

Fu, Lie, and Manh Toan Nguyen. "Orbifold Products for Higher $K$-Theory and Motivic Cohomology." Documenta Mathematica 24 (2019): 1769–810. http://dx.doi.org/10.4171/dm/715.

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33

KAUFMANN, RALPH M., and DAVID PHAM. "THE DRINFEL'D DOUBLE AND TWISTING IN STRINGY ORBIFOLD THEORY." International Journal of Mathematics 20, no. 05 (May 2009): 623–57. http://dx.doi.org/10.1142/s0129167x09005431.

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This paper exposes the fundamental role that the Drinfel'd double D(k[G]) of the group ring of a finite group G and its twists Dβ(k[G]), β ∈ Z3(G,k*) as defined by Dijkgraaf–Pasquier–Roche play in stringy orbifold theories and their twistings. The results pertain to three different aspects of the theory. First, we show that G-Frobenius algebras arising in global orbifold cohomology or K-theory are most naturally defined as elements in the braided category of D(k[G])-modules. Secondly, we obtain a geometric realization of the Drinfel'd double as the global orbifold K-theory of global quotient given by the inertia variety of a point with a G action on the one hand and more stunningly a geometric realization of its representation ring in the braided category sense as the full K-theory of the stack [pt/G]. Finally, we show how one can use the co-cycles β above to twist the global orbifold K-theory of the inertia of a global quotient and more importantly, the stacky K-theory of a global quotient [X/G]. This corresponds to twistings with a special type of two-gerbe.

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34

Basalaev, Alexey, and Atsushi Takahashi. "Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomials." Journal of Noncommutative Geometry 14, no. 3 (August 12, 2020): 861–77. http://dx.doi.org/10.4171/jncg/370.

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35

Kaufmann, Ralph M. "Global Stringy Orbifold Cohomology, K-Theory and de Rham Theory." Letters in Mathematical Physics 94, no. 2 (September 22, 2010): 165–95. http://dx.doi.org/10.1007/s11005-010-0427-z.

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36

BISWAS, INDRANIL, and MAINAK PODDAR. "CHEN–RUAN COHOMOLOGY OF SOME MODULI SPACES, II." International Journal of Mathematics 21, no. 04 (April 2010): 497–522. http://dx.doi.org/10.1142/s0129167x10006094.

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Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and ξ → X a holomorphic line bundle such that r is not a divisor of degree ξ. Let [Formula: see text] denote the moduli space of stable vector bundles over X of rank r and determinant ξ. By Γ we will denote the group of line bundles L over X such that L⊗r is trivial. This group Γ acts on [Formula: see text] by the rule (E, L) ↦ E ⊗ L. We compute the Chen–Ruan cohomology of the corresponding orbifold.

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37

Boissière, Samuel, and Marc A. Nieper-Wisskirchen. "Generating Series in the Cohomology of Hilbert Schemes of Points on Surfaces." LMS Journal of Computation and Mathematics 10 (2007): 254–70. http://dx.doi.org/10.1112/s146115700000139x.

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In the study of the rational cohomology of Hilbert schemes of points on a smooth surface, it is particularly interesting to understand the characteristic classes of the tautological bundles and the tangent bundle. In this note we pursue this study. We first collect all results appearing separately in the literature and prove some new formulas using Ohmoto's results on orbifold Chern classes on Hilbert schemes. We also explain the algorithmic counterpart of the topic: the cohomology space is governed by a vertex algebra that can be used to compute characteristic classes. We present an implementation of the vertex operators in the rewriting logic system MAUDE, and address observations and conjectures obtained after symbolic computations.

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38

Stapledon, Alan. "Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties." Proceedings of the American Mathematical Society 137, no. 12 (July 23, 2009): 4243–53. http://dx.doi.org/10.1090/s0002-9939-09-09969-9.

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39

BERGLUND, PER, BRIAN GREENE, and TRISTAN HÜBSCH. "CLASSICAL VS. LANDAU-GINZBURG GEOMETRY OF COMPACTIFICATION." Modern Physics Letters A 07, no. 20 (June 28, 1992): 1855–69. http://dx.doi.org/10.1142/s0217732392001567.

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We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth) Calabi-Yau examples in which there are obstructions to parametrizing all of the complex structure cohomology by polynomial deformations thus requiring the analysis based on exact and spectral sequences. General arguments ensure that the Landau-Ginzburg chiral ring copes with such a situation by having a non-trivial contribution from twisted sectors. Beyond the expected final agreement between the mathematical and physical approaches, we find a direct correspondence between the analysis of each, thus giving a more complete mathematical understanding of twisted sectors. Furthermore, this approach shows that physical reasoning based upon spectral flow arguments for determining the spectrum of Landau-Ginzburg orbifold models finds direct mathematical justification in Koszul complex calculations and also that careful point-field analysis continues to recover surprisingly much of the stringy features.

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40

Artal Bartolo, Enrique, José Cogolludo-Agustín, and Anatoly Libgober. "Depth of cohomology support loci for quasi-projective varieties via orbifold pencils." Revista Matemática Iberoamericana 30, no. 2 (2014): 373–404. http://dx.doi.org/10.4171/rmi/785.

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41

Volokitina, E. Y. "Cohomology of the Lie Algebra of Vector Fields on Some One-dimensional Orbifold." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 13, no. 3 (2013): 14–28. http://dx.doi.org/10.18500/1816-9791-2013-13-3-14-28.

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42

Bryan, Jim, Tom Graber, and Rahul Pandharipande. "The orbifold quantum cohomology of $\mathbb{C}^{2}/\mathbb{Z}_3$ and Hurwitz-Hodge integrals." Journal of Algebraic Geometry 17, no. 1 (January 1, 2008): 1–28. http://dx.doi.org/10.1090/s1056-3911-07-00467-5.

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43

Geuenich, Jan, and Daniel Labardini-Fragoso. "Species with Potential Arising from Surfaces with Orbifold Points of Order 2, Part II: Arbitrary Weights." International Mathematics Research Notices 2020, no. 12 (June 12, 2018): 3649–752. http://dx.doi.org/10.1093/imrn/rny090.

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Abstract Let ${\boldsymbol{\Sigma }}=(\Sigma ,\mathbb{M},\mathbb{O})$ be either an unpunctured surface with marked points and order-2 orbifold points or a once-punctured closed surface with order-2 orbifold points. For each pair $(\tau ,\omega )$ consisting of a triangulation $\tau $ of ${\boldsymbol{\Sigma }}$ and a function $\omega :\mathbb{O}\rightarrow \{1,4\}$, we define a chain complex $C_\bullet (\tau , \omega )$ with coefficients in $\mathbb{F}_2=\mathbb{Z}/2\mathbb{Z}$. Given ${\boldsymbol{\Sigma }}$ and $\omega $, we define a colored triangulation of ${\boldsymbol{\Sigma }_\omega }=(\Sigma ,\mathbb{M},\mathbb{O},\omega )$ to be a pair $(\tau ,\xi )$ consisting of a triangulation of ${\boldsymbol{\Sigma }}$ and a 1-cocycle in the cochain complex that is dual to $C_\bullet (\tau , \omega )$; the combinatorial notion of colored flip of colored triangulations is then defined as a refinement of the notion of flip of triangulations. Our main construction associates to each colored triangulation a species and a potential, and our main result shows that colored triangulations related by a flip have species with potentials (SPs) related by the corresponding SP-mutation as defined in [25]. We define the flip graph of ${\boldsymbol{\Sigma }_\omega }$ as the graph whose vertices are the pairs $(\tau ,x)$ consisting of a triangulation $\tau $ and a cohomology class $x\in H^1(C^\bullet (\tau , \omega ))$, with an edge connecting two such pairs, $(\tau ,x)$ and $(\sigma ,z),$ if and only if there exist 1-cocycles $\xi \in x$ and $\zeta \in z$ such that $(\tau ,\xi )$ and $(\sigma ,\zeta )$ are colored triangulations related by a colored flip; then we prove that this flip graph is always disconnected provided the underlying surface $\Sigma $ is not contractible. In the absence of punctures, we show that the Jacobian algebras of the SPs constructed are finite-dimensional and that whenever two colored triangulations have the same underlying triangulation, the Jacobian algebras of their associated SPs are isomorphic if and only if the underlying 1-cocycles have the same cohomology class. We also give a full classification of the nondegenerate SPs one can associate to any given pair $(\tau ,\omega )$ over cyclic Galois extensions with certain roots of unity. The species constructed here are species realizations of the $2^{|\mathbb{O}|}$ skew-symmetrizable matrices that Felikson–Shapiro–Tumarkin associated in [17] to any given triangulation of ${\boldsymbol{\Sigma }}$. In the prequel [25] of this paper we constructed a species realization of only one of these matrices, but therein we allowed the presence of arbitrarily many punctures.

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44

HONG, SEUNG-MOON, ERIC ROWELL, and ZHENGHAN WANG. "ON EXOTIC MODULAR TENSOR CATEGORIES." Communications in Contemporary Mathematics 10, supp01 (November 2008): 1049–74. http://dx.doi.org/10.1142/s0219199708003162.

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It has been conjectured that every (2 + 1)-TQFT is a Chern-Simons-Witten (CSW) theory labeled by a pair (G, λ), where G is a compact Lie group, and λ ∈ H4(BG; ℤ) a cohomology class. We study two TQFTs constructed from Jones' subfactor theory which are believed to be counterexamples to this conjecture: one is the quantum double of the even sectors of the E6subfactor, and the other is the quantum double of the even sectors of the Haagerup subfactor. We cannot prove mathematically that the two TQFTs are indeed counterexamples because CSW TQFTs, while physically defined, are not yet mathematically constructed for every pair (G, λ). The cases that are constructed mathematically include: (1) G is a finite group — the Dijkgraaf-Witten TQFTs; (2) G is torus Tn; (3) G is a connected semi-simple Lie group — the Reshetikhin-Turaev TQFTs.We prove that the two TQFTs are not among those mathematically constructed TQFTs or their direct products. Both TQFTs are of the Turaev-Viro type: quantum doubles of spherical tensor categories. We further prove that neither TQFT is a quantum double of a braided fusion category, and give evidence that neither is an orbifold or coset of TQFTs above. Moreover, representation of the braid groups from the half E6TQFT can be used to build universal topological quantum computers, and the same is expected for the Haagerup case.

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45

Moerdijk, I., and D. A. Pronk. "Simplicial cohomology of orbifolds." Indagationes Mathematicae 10, no. 2 (1999): 269–93. http://dx.doi.org/10.1016/s0019-3577(99)80021-4.

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46

Pardon, John. "Enough vector bundles on orbispaces." Compositio Mathematica 158, no. 11 (November 2022): 2046–81. http://dx.doi.org/10.1112/s0010437x22007783.

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We show that every orbispace satisfying certain mild hypotheses has ‘enough’ vector bundles. It follows that the $K$ -theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth orbifolds and derived smooth orbifolds also follow.

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47

Hassani, Feysal, and Negin Salehi Oroozaki. "The First Hochschild Cohomology of Square Algebras With it's Stability." Journal of Mathematics Research 9, no. 4 (July 25, 2017): 200. http://dx.doi.org/10.5539/jmr.v9n4p200.

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In this paper, we study on a special case of generalized matrix algebra that we call it square algebra. According to that Hochschild cohomology play a significant role in Geometry for example in orbifolds, we study the first Hochschild cohomology of the square algebra the vanishing of its.

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48

Adem, Alejandro, and Jianzhong Pan. "Toroidal orbifolds, gerbes and group cohomology." Transactions of the American Mathematical Society 358, no. 9 (April 11, 2006): 3969–83. http://dx.doi.org/10.1090/s0002-9947-06-04017-7.

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49

Takeuchi, Yoshihiro, and Misako Yokoyama. "The ws-singular cohomology of orbifolds." Topology and its Applications 154, no. 8 (April 2007): 1664–78. http://dx.doi.org/10.1016/j.topol.2006.12.009.

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50

Du, Cheng-Yong, and Xiaojuan Zhao. "Spark and Deligne-Beilinson cohomology on orbifolds." Journal of Geometry and Physics 104 (June 2016): 277–90. http://dx.doi.org/10.1016/j.geomphys.2016.02.011.

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