2007/12/31 by David Chataur, Chataur, David, Luc Menichi +1 · 2 citations
Mathematics · Physics and Astronomy · #18D50 #55N91 #55P35 #55P48 #55R12 #55R35 #55R40 #57R56 #58D29 #81T40 #81T45 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.QA #msc:18D50 #msc:55N91 #msc:55P35 #msc:55P48 #msc:55R12 #msc:55R35 #msc:55R40 #msc:57R56 #msc:58D29 #msc:81T40 #msc:81T45
paper · pdf · doi:10.48550/arxiv.0801.0174
53 pages. Section 3 on Props and fields theories rewritten. Section 4 expanded in new sections 4, 5, 6 and 7, to fix orientation problems, finite groups case detailed in section 7. Appendix on signs added. The rest of the sections almost unchanged. Some slight improvements on some results. For example, the BV-algebra is valid over any principal ideal domain
openalex publication_date 2007/12/31 · arxiv created 2009/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let LBG:=map(S1,BG) be the free loop space of BG i.e. the space of continuous maps from the circle S1 to BG. The purpose of this paper is to study the singular homology H_*(\mathcal LBG) of this loop space. We prove that when taken with coefficients in a field the homology of \mathcal LBG is a homological conformal field theory. As a byproduct of our main theorem, we get a Batalin-Vilkovisky algebra structure on the cohomology H^*(\mathcal LBG). We also prove an algebraic version of this result by showing that the Hochschild cohomology HH^*(S_* (G),S_*(G)) of the singular chains of G is a Batalin-Vilkovisky algebra.