Infinity Structure of Poincare Duality Spaces
| dc.creator | Tradler, Thomas | |
| dc.creator | Zeinalian, Mahmoud | |
| dc.creator | Sullivan, Dennis | |
| dc.date | 2003-09-28 | |
| dc.date | 2006-11-01 | |
| dc.date.accessioned | 2026-07-07T12:50:36Z | |
| dc.date.available | 2026-07-07T12:50:36Z | |
| dc.description | We show that the complex $C_\bullet X$ of rational simplicial chains on a compact and triangulated Poincaré duality space $X$ of dimension $d$ is an A$_\infty$ coalgebra with $\infty$ duality. This is the structure required for an A$_\infty$ version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology $HH^{\bullet+d} (C^\bullet X, C_\bullet X)$ of the cochain algebra $C^\bullet X$ with values in $C_\bullet X$ has a BV structure. This implies, if $X$ is moreover simply connected, that the shifted homology $H_{\bullet+d}LX$ of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of $\infty$ structures. | |
| dc.description | 28 pages, revised version, new appendix by Dennis Sullivan added | |
| dc.identifier | https://arxiv.org/abs/math/0309455 | |
| dc.identifier | http://arxiv.org/abs/math/0309455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222730 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Quantum Algebra | |
| dc.title | Infinity Structure of Poincare Duality Spaces | |
| dc.type | text |