String topology of classifying spaces

Chataur, David; Menichi, Luc

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1515/CRELLE.2011.140

Titre :

String topology of classifying spaces

Auteur(s) :

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

Titre de la revue :

Journal für die reine und angewandte Mathematik

Pagination :

1 - 45

Éditeur :

Walter de Gruyter

Date de publication :

2012

ISSN :

0075-4102

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [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 ...
Lire la suite ><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>Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

0801.0174
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