String topology for loop stacks

Kai Behrend; Grégory Ginot; Behrang Noohi; Ping Xu

doi:10.1016/j.crma.2006.10.006

Topology/Geometry

String topology for loop stacks
[Topologie des cordes pour les lacets libres d'un champ]

Présenté par : Charles-Michel Marle

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

Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 247-252.

Résumé
Abstract

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 $H_{•} (L X) = H_{• + d} (L X)$ 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 $H_{•} (L X) = H_{• + d} (L X)$ admits a BV algebra structure.

Reçu le : 2006-08-09
Accepté le : 2006-10-11
Publié le : 2007-02-06

DOI : 10.1016/j.crma.2006.10.006

Affiliations des auteurs :

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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     author = {Kai Behrend and Gr\'egory Ginot and Behrang Noohi and Ping Xu},
     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},
}

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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/

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