On munit les groupes d'homologie du champ des lacets libres d'un champ orienté d'un produit et d'un coproduit induisant une structure d'algèbre de Frobenius. De plus, l'homologie en degrés décalés est une algèbre BV.
We prove that the homology groups of the free loop stack of an oriented stack are equipped with a canonical loop product and coproduct, which makes it into a Frobenius algebra. Moreover, the shifted homology admits a BV algebra structure.
Accepté le :
Publié le :
@article{CRMATH_2007__344_4_247_0, author = {Behrend, Kai and Ginot, Gr\'egory and Noohi, Behrang and Xu, Ping}, title = {String topology for loop stacks}, journal = {Comptes Rendus. Math\'ematique}, pages = {247--252}, publisher = {Elsevier}, volume = {344}, number = {4}, year = {2007}, doi = {10.1016/j.crma.2006.10.006}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.10.006/} }
TY - JOUR AU - Behrend, Kai AU - Ginot, Grégory AU - Noohi, Behrang AU - Xu, Ping TI - String topology for loop stacks JO - Comptes Rendus. Mathématique PY - 2007 SP - 247 EP - 252 VL - 344 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.10.006/ DO - 10.1016/j.crma.2006.10.006 LA - en ID - CRMATH_2007__344_4_247_0 ER -
%0 Journal Article %A Behrend, Kai %A Ginot, Grégory %A Noohi, Behrang %A Xu, Ping %T String topology for loop stacks %J Comptes Rendus. Mathématique %D 2007 %P 247-252 %V 344 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2006.10.006/ %R 10.1016/j.crma.2006.10.006 %G en %F CRMATH_2007__344_4_247_0
Behrend, Kai; Ginot, Grégory; Noohi, Behrang; Xu, Ping. String topology for loop stacks. Comptes Rendus. Mathématique, Tome 344 (2007) no. 4, pp. 247-252. doi : 10.1016/j.crma.2006.10.006. http://archive.numdam.org/articles/10.1016/j.crma.2006.10.006/
[1] K. Behrend, G. Ginot, B. Noohi, P. Xu, String product for inertia stacks, preprint
[2] K. Behrend, G. Ginot, B. Noohi, P. Xu, Frobenius structure for inertia stacks, preprint
[3] String topology | arXiv
[4] A polarized view of string topology, Topology, Geometry and Quantum Field Theory, London Math. Soc. Lecture Note Ser., vol. 308, 2004, pp. 127-154
[5] A homotopy theoretic realization of string topology, Math. Ann., Volume 324 (2002) no. 4, pp. 773-798
[6] Notes on string topology, String Topology and Cyclic Homology, Adv. Courses Math. CRM Barcelona, Birkhäuser, Basel, 2006, pp. 1-95
[7] Orbifold string topology | arXiv
[8] Lie groupoids, sheaves and cohomology, Poisson Geometry, Deformation Quantisation and Group Representations, London Math. Soc. Lecture Note Ser., vol. 323, 2005, pp. 145-272
[9] Foundations of topological stacks, I | arXiv
Cité par Sources :