Higher string topology on general spaces
| dc.creator | Hu, P. | |
| dc.date | 2004-01-08 | |
| dc.date.accessioned | 2026-07-07T05:04:26Z | |
| dc.date.available | 2026-07-07T05:04:26Z | |
| dc.description | In this paper, I give a generalized analogue of the string topology results of Chas and Sullivan, and of Cohen and Jones. For a finite simplicial complex $X$ and $k \geq 1$, I construct a spectrum $Maps(S^k, X)^{S(X)}$, and show that the corresponding chain complex is naturally homotopy equivalent to an algebra over the $(k+1)$-dimensional unframed little disk operad $\mathcal{C}_{k+1}$. I also prove Kontsevich's conjecture that the Quillen cohomology of a based $\mathcal{C}_k$-algebra (in the category of chain complexes) is equivalent to a shift of its Hochschild cohomology, as well as prove that the operad $C_{\ast}\mathcal{C}_k$ is Koszul-dual to itself up to a shift in the derived category. This gives one a natural notion of (derived) Koszul dual $C_{\ast}\mathcal{C}_k$-algebras. I show that the cochain complex of $X$ and the chain complex of $Ω^k X$ are Koszul dual to each other as $C_{\ast}\mathcal{C}_k$-algebras, and that the chain complex of $Maps(S^k, X)^{S(X)}$ is naturally equivalent to their (equivalent) Hochschild cohomology in the category of $C_{\ast}\mathcal{C}_k$-algebras. | |
| dc.identifier | https://arxiv.org/abs/math/0401081 | |
| dc.identifier | http://arxiv.org/abs/math/0401081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69806 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P48 (primary), 16E40, 55N45, 18D50 (secondary) | |
| dc.title | Higher string topology on general spaces | |
| dc.type | text |