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Article Dans Une Revue Commentarii Mathematici Helvetici Année : 2009

String topology for spheres



Let M be a compact oriented d-dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin-Vilkovisky algebra on H*(LM). Extending work of Cohen, Jones and Yan, we compute this Batalin-Vilkovisky algebra structure when M is a sphere Sd, d ≥ 1. In particular, we show that H*(LS2;{F}2) and the Hochschild cohomology HH*(H*(S2);H*(S2)) 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 H*(Ω2S3;{F}2) that we compute in the Appendix.

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Dates et versions

hal-03040209 , version 1 (04-12-2020)


  • HAL Id : hal-03040209 , version 1
  • OKINA : ua158


Luc Menichi. String topology for spheres. Commentarii Mathematici Helvetici, 2009, 84 (1), pp.135 - 157. ⟨hal-03040209⟩
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