Spaces of self-equivalences and free loops spaces
| dc.creator | Felix, Yves | |
| dc.creator | Thomas, Jean-Claude | |
| dc.date | 2002-04-11 | |
| dc.date.accessioned | 2026-07-07T04:47:38Z | |
| dc.date.available | 2026-07-07T04:47:38Z | |
| dc.description | Let M be a simply-connected closed oriented N-dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras $Ψ: H_\ast (Ω{aut}_1 M) \to H_{\ast +N}(M^{S^1})$ where $H_\ast (M^{S^1})$ is the loop algebra defined by Chas-Sullivan. As usual ${aut}_1 X$ (resp. $ΩX$) denotes the monoid of the self-equivalences homotopic to the identity map (resp. the space of based loops) of the space X. Moreover, if $\bk$ is of characteristic zero, $Ψ$ yields isomorphisms $π_n(Ω{aut}_1 M) \otimes \bk \cong \hH^{n+N}_{(1)}$ where $\displaystyle \oplus_{l=1}^\infty \hH^n_{(l)}$ denotes the Hodge decomposition on $H^\ast (M ^{S^1})$. | |
| dc.identifier | https://arxiv.org/abs/math/0204152 | |
| dc.identifier | http://arxiv.org/abs/math/0204152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63794 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P35; 55P62;55P10 | |
| dc.title | Spaces of self-equivalences and free loops spaces | |
| dc.type | text |