String topology prospectra and Hochschild cohomology

dc.creatorGruher, Kate
dc.creatorWesterland, Craig
dc.date2007-10-07
dc.date2007-11-10
dc.date.accessioned2026-07-07T08:41:40Z
dc.date.available2026-07-07T08:41:40Z
dc.descriptionWe 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.description19 pages. Comments welcome. References added, some statements clarified
dc.identifierhttps://arxiv.org/abs/0710.1445
dc.identifierhttp://arxiv.org/abs/0710.1445
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141746
dc.subjectAlgebraic Topology
dc.subjectQuantum Algebra
dc.subject55R10; 55R12; 55P35; 55P25; 16E40
dc.titleString topology prospectra and Hochschild cohomology
dc.typetext

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