String topology of classifying spaces

Chataur, David; Menichi, Luc

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1515/CRELLE.2011.140

Title :

String topology of classifying spaces

Author(s) :

Chataur, David [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Menichi, Luc [Auteur]
Laboratoire Angevin de Recherche en Mathématiques [LAREMA]

Journal title :

Journal für die reine und angewandte Mathematik

Pages :

1 - 45

Publisher :

Walter de Gruyter

Publication date :

2012

ISSN :

0075-4102

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

<p>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 ...
Show more ><p>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)</p>Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

0801.0174
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