Relevant bibliographies by topics / Orbifold cohomology

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Orbifold cohomology'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Orbifold cohomology"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Orbifold cohomology"

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Perroni, Fabio. "Orbifold Cohomology of ADE-singularities." Doctoral thesis, SISSA, 2005. http://hdl.handle.net/20.500.11767/4241.

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In Chapter 1 we collect some basic definitions on orbifolds, morphisms of orbifolds and orbifold vector bundles. In Chapter 3 we first review the definition of orbifold cohomology ring for a complex orbifold, then we state the cohomological crepant resolution conjecture as given by Ruan in [52]. In Chapter 4 we define orbifolds with transversal ADE-singularities, see Definition 4.2.5. Then we give a description of the twisted sectors in general. Finally we specialize to orbifolds with transversal A_n-singularities and, under the technical assumption of trivial monodromy, we compute the orbifold cohomology ring. In Chapter 5 we study the crepant resolution. We first show that any variety with transversal ADE-singularities Y has a unique crepant resolution p : Z --> Y, Proposition 5. 2 .1. Then we restrict our attention to the case of transversal An-singularities and trivial monodromy and we give an explicit description of the cohomology ring of Z. Chapter 6 contains the computations of the Gromov-Witten invariants of Z in the A_n case. We also give a description of the quantum corrected cohomology ring of Z. In Chapter 7 we prove Ruan's conjecture in the Ai case and, in the A2 case with minor modifications.
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Wren, Andrew. "The geometry of complex orbifolds." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386824.

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Duman, Ali Nabi. "Fusion algebras and cohomology of toroidal orbifolds." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/23510.

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In this thesis we exhibit an explicit non-trivial example of the twisted fusion algebra for a particular finite group. The product is defined for the third power of modulo two group via the pairing of projective representations where the three cocycles are chosen using the inverse transgression map. We find the rank of the fusion algebra as well as the relation between its basis elements. We also give some applications to topological gauge theories. We next show that the twisted fusion algebra of the third power of modulo p group is isomorphic to the non-twisted fusion algebra of the extraspecial p-group of order p³ and exponent p. The final point of my thesis is to explicitly compute the cohomology groups of toroidal orbifolds which are the quotient spaces obtained by the action of modulo p group on the k-dimensional torus. We compute the particular case where the action is induced by the n-th power of augmentation ideal.
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Mann, Etienne. "Cohomologie quantique orbifolde des espaces projectifs à poids." Phd thesis, Université Louis Pasteur - Strasbourg I, 2005. http://tel.archives-ouvertes.fr/tel-00011651.

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En 2001, Barannikov a montré que la variété de Frobenius provenant de la cohomologie quantique de l'espace projectif complexe est isomorphe à la variété le Frobenius associée à un polynôme de Laurent.

L'objectif de cette thèse est de généraliser ce résultat. Plus précisément, nous montrons, modulo une conjecture sur la valeur de certains invariants de Gromov-Witten orbifold, que la structure de Frobenius obtenue sur la cohomologie quantique orbifolde de l'espace projectif à poids est isomorphe à celle obtenue à partir d'un certain polynôme de Laurent.
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Greene, Ryan M. "THE DEFORMATION THEORY OF DISCRETE REFLECTION GROUPS AND PROJECTIVE STRUCTURES." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1374156914.

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Grivaux, Julien. "Quelques problèmes de géométrie complexe et presque complexe." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00460334.

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Le travail effectué dans cette thèse consiste à construire et adapter dans d'autres cadres des objets issus de la géométrie algébrique. Nous nous intéressons d'abord à la théorie des classes de Chern pour les faisceaux cohérents. Sur les variétés projectives, elle est complètement achevée dans les anneaux de Chow grâce à l'existence de résolutions globales localement libres et se ramène formellement à la théorie pour les fibrés. Un résultat de Voisin montre que ces résolutions n'existent pas toujours sur des variétés complexes compactes générales. Nous construisons ici par récurrence sur la dimension de la variété de base des classes de Chern en cohomologie de Deligne rationnelle pour les faisceaux analytiques cohérents en imposant la formule de Grothendieck-Riemann-Roch pour les immersions et en utilisant des méthodes de dévissage. Ces classes sont les seules à vérifier la formule de fonctorialité par pull-back, la formule de Whitney et la formule de Grothendieck-Riemann-Roch pour les immersions; elles coïncident donc avec les classes topologiques et les classes d'Atiyah. Elles vérifient aussi le théorème de Grothendieck-Riemann-Roch pour les morphismes projectifs. Notre second travail est l'étude des schémas de Hilbert ponctuels d'une variété symplectique ou presque complexe de dimension 4. Ils ont été construits par Voisin et généralisent les schémas de Hilbert connus pour les surfaces projectives. En utilisant les structures complexes relatives intégrables introduites dans la construction de Voisin, nous pouvons étendre au cas presque complexe ou symplectique la théorie classique. Nous calculons les nombres de Betti, nous construisons les opérateurs de Nakajima, nous étudions l'anneau de cohomologie et la classe de cobordisme de ces schémas de Hilbert, et nous prouvons dans ce contexte un cas particulier de la conjecture de la résolution crêpante de Ruan.
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Uribe, Bernardo. "Twisted k-theory and orbifold cohomology of the symmetric product /." 2002. http://www.library.wisc.edu/databases/connect/dissertations.html.

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Books on the topic "Orbifold cohomology"

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Basterra, Maria, Kristine Bauer, Kathryn Hess, and Brenda Johnson. Women in topology: Collaborations in homotopy theory : WIT, Women in Topology Workshop, August 18-23, 2013, Banff International Research Station, Banff, Alberta, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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Huybrechts, D. Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.001.0001.

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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
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Book chapters on the topic "Orbifold cohomology"

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Barakat, Mohamed, and Simon Görtzen. "Simplicial Cohomology of Smooth Orbifolds in GAP." In Mathematical Software – ICMS 2010, 46–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15582-6_9.

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Wassermann, A. J. "Cyclic cohomology of algebras of smooth functions on orbifolds." In Operator Algebras and Applications, 229–44. Cambridge University Press, 1989. http://dx.doi.org/10.1017/cbo9780511662270.013.

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Conference papers on the topic "Orbifold cohomology"

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LUPERCIO, ERNESTO, and BERNARDO URIBE. "DELIGNE COHOMOLOGY FOR ORBIFOLDS, DISCRETE TORSION AND B-FIELDS." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705068_0010.

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