Academic literature on the topic 'DG-Manifolds'
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Journal articles on the topic "DG-Manifolds":
Cheng, Jiahao, Zhuo Chen, and Dadi Ni. "Hopf algebras arising from dg manifolds." Journal of Algebra 584 (October 2021): 19–68. http://dx.doi.org/10.1016/j.jalgebra.2021.05.004.
Ciocan-Fontanine, Ionuţ, and Mikhail Kapranov. "Virtual fundamental classes via dg–manifolds." Geometry & Topology 13, no. 3 (March 16, 2009): 1779–804. http://dx.doi.org/10.2140/gt.2009.13.1779.
Stiénon, Mathieu, and Ping Xu. "Fedosov dg manifolds associated with Lie pairs." Mathematische Annalen 378, no. 1-2 (July 26, 2020): 729–62. http://dx.doi.org/10.1007/s00208-020-02012-6.
Laurent-Gengoux, Camille, Mathieu Stiénon, and Ping Xu. "Poincaré–Birkhoff–Witt isomorphisms and Kapranov dg-manifolds." Advances in Mathematics 387 (August 2021): 107792. http://dx.doi.org/10.1016/j.aim.2021.107792.
Seol, Seokbong, Mathieu Stiénon, and Ping Xu. "Dg Manifolds, Formal Exponential Maps and Homotopy Lie Algebras." Communications in Mathematical Physics 391, no. 1 (February 24, 2022): 33–76. http://dx.doi.org/10.1007/s00220-021-04265-x.
Uribe, Bernardo. "Group Actions on DG-Manifolds and Exact Courant Algebroids." Communications in Mathematical Physics 318, no. 1 (January 23, 2013): 35–67. http://dx.doi.org/10.1007/s00220-013-1669-2.
Bernardara, Marcello, Matilde Marcolli, and Gonçalo Tabuada. "Some remarks concerning Voevodsky’s nilpotence conjecture." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 738 (May 1, 2018): 299–312. http://dx.doi.org/10.1515/crelle-2015-0068.
Lupercio, Ernesto, Camilo Rengifo, and Bernardo Uribe. "T-duality and exceptional generalized geometry through symmetries of dg-manifolds." Journal of Geometry and Physics 83 (September 2014): 82–98. http://dx.doi.org/10.1016/j.geomphys.2014.05.012.
GRIBACHEVA, DOBRINKA. "A NATURAL CONNECTION ON A BASIC CLASS OF RIEMANNIAN PRODUCT MANIFOLDS." International Journal of Geometric Methods in Modern Physics 09, no. 07 (September 7, 2012): 1250057. http://dx.doi.org/10.1142/s0219887812500570.
Pridham, J. P. "Representability of derived stacks." Journal of K-Theory 10, no. 2 (January 31, 2012): 413–53. http://dx.doi.org/10.1017/is012001005jkt179.
Dissertations / Theses on the topic "DG-Manifolds":
Louis, Ruben. "Les algèbres supérieures universelles des espaces singuliers et leurs symétries." Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0165.
This thesis breaks into two main parts.1) We show that there is an equivalence of categories between Lie-Rinehart algebras over a commutative algebra O and homotopy equivalence classes of negatively graded acyclic Lie infinity-algebroids. Therefore, this result makes sense of the universal Lie infinity-algebroid of every singular foliation,without any additional assumption, and for Androulidakis-Zambon singular Lie algebroids. This extends to a purely algebraic setting the construction of the universal Q-manifold of a locally real analytic singular foliation. Also, to any ideal I of O preserved by the anchor map of a Lie-Rinehart algebra A, we associate a homotopy equivalence class of negatively graded Lie infinity-algebroids over complexes computing Tor_O(A,O/I). Several explicit examples are given.2) The second part is dedicated to some applications of the results on Lie-Rinehart algebras.a. We associate to any affine variety a universal Lie infinity-algebroid of the Lie-Rinehart algebra of its vector fields. We study the effect of some common operations on affine varieties such as blow-ups, germs at a point, etc.b. We give an interpretation of the blow-up of a singular foliation F in the sense of Omar Mohsen in term of the universal Lie infinity-algebroid of F.c. We introduce the notion of longitudinal vector fields on a graded manifold over a singular foliation, and study their cohomology. We prove that the cohomology groups of the latter vanish.d. We study symmetries of singular foliations through universal Lie infinity-algebroids. More precisely, we prove that a weak symmetry action of a Lie algebra g on a singular foliation F (which is morally an action of g on the leaf space M/F) induces a unique up to homotopy Lie infinity-morphism from g to the Differential Graded Lie Algebra (DGLA) of vector fields on a universal Lie infinity-algebroid of F. We deduce from this general result several geometrical consequences. For instance, we give an example of a Lie algebra action on an affine sub-variety which cannot be extended on the ambient space. Last, we present the notion of tower of bi-submersions over a singular foliation and lift symmetries to those