A duality between string topology and the fusion product in equivariant K-theory
| dc.creator | Gruher, Kate | |
| dc.date | 2006-08-14 | |
| dc.date.accessioned | 2026-07-07T07:21:47Z | |
| dc.date.available | 2026-07-07T07:21:47Z | |
| dc.description | Let G be a compact Lie group. Let E be a principal G-bundle over a closed manifold M, and Ad(E) its adjoint bundle. In this paper we describe a new Frobenius algebra structure on h_*(Ad(E)), where h_* is an appropriate generalized homology theory. Recall that a Frobenius algebra has both a product and a coproduct. The product in this new Frobenius algebra is induced by the string topology product. In particular, the product can be defined when G is any topological group and in the case that E is contractible it is precisely the Chas-Sullivan string product on H_*(LM). We will show that the coproduct is induced by the Freed-Hopkins-Teleman fusion product. Indeed, when M is replaced by BG and h_* is K-theory the coproduct is the completion of the Freed-Hopkins-Teleman fusion structure. We will then show that this duality between the string and fusion products is realized by a Spanier-Whitehead duality between certain Thom spectra of virtual bundles over Ad(E). | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608366 | |
| dc.identifier | http://arxiv.org/abs/math/0608366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115426 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55R10; 55P35; 55P25 | |
| dc.title | A duality between string topology and the fusion product in equivariant K-theory | |
| dc.type | text |