String topology for spheres
| dc.creator | Menichi, Luc | |
| dc.creator | Gaudens, Gerald | |
| dc.date | 2006-09-11 | |
| dc.date | 2007-11-13 | |
| dc.date.accessioned | 2026-07-07T12:50:38Z | |
| dc.date.available | 2026-07-07T12:50:38Z | |
| dc.description | Let $M$ be a compact oriented $d$-dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin-Vilkovisky algebra on $\mathbb{H}_*(LM)$. Extending work of Cohen, Jones and Yan, we compute this Batalin-Vilkovisky algebra structure when $M$ is a sphere $S^d$, $d\geq 1$. In particular, we show that $\mathbb{H}_*(LS^2;\mathbb{F}_2)$ and the Hochschild cohomology $HH^{*}(H^*(S^2);H^*(S^2))$ 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 $H_*(Ω^2 S^3;\mathbb{F}_2)$ that we compute in the Appendix. | |
| dc.description | 22 pages. Minor corrections. An appendix by Gerald Gaudens and Luc Menichi has been added. Final version. To appear in Comment. Math. Helv | |
| dc.identifier | https://arxiv.org/abs/math/0609304 | |
| dc.identifier | http://arxiv.org/abs/math/0609304 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222743 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.title | String topology for spheres | |
| dc.type | text |