String topology prospectra and Hochschild cohomology
| dc.creator | Gruher, Kate | |
| dc.creator | Westerland, Craig | |
| dc.date | 2007-10-07 | |
| dc.date | 2007-11-10 | |
| dc.date.accessioned | 2026-07-07T08:41:40Z | |
| dc.date.available | 2026-07-07T08:41:40Z | |
| dc.description | We study string topology for classifying spaces of connected compact Lie groups, drawing connections with Hochschild cohomology and equivariant homotopy theory. First, for a compact Lie group $G$, we show that the string topology prospectrum $LBG^{-TBG}$ is equivalent to the homotopy fixed-point prospectrum for the conjugation action of $G$ on itself, $G^{hG}$. Dually, we identify $LBG^{-ad}$ with the homotopy orbit spectrum $(DG)_{hG}$, and study ring and co-ring structures on these spectra. Finally, we show that in homology, these products may be identified with the Gerstenhaber cup product in the Hochschild cohomology of $C^*(BG)$ and $C_*(G)$, respectively. These, in turn, are isomorphic via Koszul duality. | |
| dc.description | 19 pages. Comments welcome. References added, some statements clarified | |
| dc.identifier | https://arxiv.org/abs/0710.1445 | |
| dc.identifier | http://arxiv.org/abs/0710.1445 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141746 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Quantum Algebra | |
| dc.subject | 55R10; 55R12; 55P35; 55P25; 16E40 | |
| dc.title | String topology prospectra and Hochschild cohomology | |
| dc.type | text |