Premium
String topology prospectra and Hochschild cohomology
Author(s) -
Gruher Kate,
Westerland Craig
Publication year - 2008
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtn025
Subject(s) - hochschild homology , mathematics , homotopy , cohomology , topology (electrical circuits) , homology (biology) , cohomology ring , pure mathematics , equivariant cohomology , string (physics) , lie group , combinatorics , mathematical physics , biochemistry , chemistry , gene
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, S 0 [ 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.