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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2012

String topology of classifying spaces

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David Chataur

Résumé

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*(ℒBG) of this loop space. We prove that when taken with coefficients in a field the homology of 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*(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.Comments (0)

Dates et versions

hal-03031594 , version 1 (30-11-2020)

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David Chataur, Luc Menichi. String topology of classifying spaces. Journal für die reine und angewandte Mathematik, 2012, 2012 (669), pp.1 - 45. ⟨10.1515/CRELLE.2011.140⟩. ⟨hal-03031594⟩
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