Topology/Geometry
String topology for loop stacks
Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 247-252.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.10.006
Behrend, Kai 1; Ginot, Grégory 2; Noohi, Behrang 3; Xu, Ping 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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Behrend, Kai; Ginot, Grégory; Noohi, Behrang; Xu, Ping. String topology for loop stacks. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 247-252. doi : 10.1016/j.crma.2006.10.006. http://www.numdam.org/articles/10.1016/j.crma.2006.10.006/

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