Hochschild cohomology and string topology of global quotient orbifolds
type: Item
instance of: scholarly article
title: Hochschild cohomology and string topology of global quotient orbifolds
zbMATH Open document ID: 1250.55006
author: Andrés Angel
author: Erik Backelin
author: Bernardo Uribe
published in: Journal of Topology
publication date: 2012-09-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.4427
Mathematics Subject Classification ID: 55P50
Mathematics Subject Classification ID: 57R18
zbMATH DE Number: 6084065
zbMATH Keywords: string topology
zbMATH Keywords: orbifold
MaRDI profile type: Publication
OpenAlex ID: W3105897668
arXiv ID: 1004.4427
DOI: 10.1112/JTOPOL/JTS016
review text: In this paper the authors investigate string topology of global quotient orbifolds. Let \(M\) be a connected simply connected, closed manifold, \(G\) be a finite group and \([M/G]\) be a global quotient orbifold whose natural free loop space is a loop groupoid, denoted by \([PGM/G]\). It turns out that the Borel construction \(P_GM \times_G EG\) is homotopy equivalent to the space of free loops on the Borel construction \(M \times_G EG\). With this equivalence at hand it is natural to ask: Can the homology \(H_\ast ( L(M \times_G EG); \mathbb Z)\) be endowed with structure of a Batalin-Vilkosky algebra and is there a relation between this structure and the Hochschild cohomology of some specific DG algebra? The paper is devoted to positively answering these two questions. The answer to the second question begins with the important observation: the ring of singular cochains \(C * (M \times_G EG)\) is not the `good candidate' for this specific DG algebra.
reviewed by: Jean-Claude Thomas
description: scientific article; zbMATH DE number 6084065