String topology for spheres

  • Luc Menichi

    Université d'Angers, France

Abstract

Let be a compact oriented -dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin–Vilkovisky algebra on . Extending work of Cohen, Jones and Yan, we compute this Batalin–Vilkovisky algebra structure when is a sphere , . In particular, we show that and the Hochschild cohomology are surprisingly not isomorphic as Batalin–Vilkovisky algebras, although we prove that, as expected, the underlying Gerstenhaber algebras are isomorphic. The proof requires the knowledge of the Batalin–Vilkovisky algebra that we compute in the Appendix.

Cite this article

Luc Menichi, String topology for spheres. Comment. Math. Helv. 84 (2009), no. 1, pp. 135–157

DOI 10.4171/CMH/155