Comptes Rendus
Topology/Geometry
String topology for loop stacks
[Topologie des cordes pour les lacets libres d'un champ]
Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 247-252.

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 H(LX)=H+d(LX) 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 H(LX)=H+d(LX) admits a BV algebra structure.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.10.006

Kai Behrend 1 ; Grégory Ginot 2 ; Behrang Noohi 3 ; Ping Xu 4

1 Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
2 École normale supérieure de Cachan et université Paris 13, CMLA, 61, avenue du Président Wilson, 94230 Cachan cedex, France
3 Max Planck Institut für Mathematik, Vivastsgasse 7, 53111 Bonn, Germany
4 Pennsylvania State University, 210 McAllister Building, University Park, PA 16802, USA
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Kai Behrend; Grégory Ginot; Behrang Noohi; Ping Xu. String topology for loop stacks. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 247-252. doi : 10.1016/j.crma.2006.10.006. https://comptes-rendus.academie-sciences.fr/mathematique/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] M. Chas; D. Sullivan String topology | arXiv

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[5] R. Cohen; J. Jones A homotopy theoretic realization of string topology, Math. Ann., Volume 324 (2002) no. 4, pp. 773-798

[6] R. Cohen; A. Voronov Notes on string topology, String Topology and Cyclic Homology, Adv. Courses Math. CRM Barcelona, Birkhäuser, Basel, 2006, pp. 1-95

[7] E. Lupercio; B. Uribe; M. Xicoténcatl Orbifold string topology | arXiv

[8] I. Moerdijk; J. Mrčun 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] B. Noohi Foundations of topological stacks, I | arXiv

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