Loop coproducts in string topology and triviality of higher genus TQFT operations
| dc.creator | Tamanoi, Hirotaka | |
| dc.date | 2007-06-08 | |
| dc.date | 2008-11-16 | |
| dc.date.accessioned | 2026-07-07T10:18:14Z | |
| dc.date.available | 2026-07-07T10:18:14Z | |
| dc.description | Cohen and Godin constructed positive boundary topological quantum field theory (TQFT) structure on the homology of free loop spaces of oriented closed smooth manifolds by associating a certain operations called string operations to orientable surfaces with parametrized boundaries. We show that all TQFT string operations associated to surfaces of genus at least one vanish identically. This is a simple consequence of properties of the loop coproduct which will be discussed in detail. One interesting property is that the loop coproduct is nontrivial only on the degree $d$ homology group of the connected component of $LM$ consisting of contractible loops, where $d=\dim M$, with values in the degree 0 homology group of constant loops. Thus the loop coproduct behaves in a dramatically simpler way than the loop product. | |
| dc.description | Version 3: 15 pages, reorganizartion of the paper, part (2) added to Theorem B, references added, improvement on exposition | |
| dc.identifier | https://arxiv.org/abs/0706.1276 | |
| dc.identifier | http://arxiv.org/abs/0706.1276 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174125 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P35 | |
| dc.title | Loop coproducts in string topology and triviality of higher genus TQFT operations | |
| dc.type | text |