On 3-dimensional homotopy quantum field theory. I.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1254.57012
DOI: 10.1142/S0129167X12500942
author: Alexis Virelizier
author: Vladimir Turaev
published in: International Journal of Mathematics
publication date: 2012-09-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.6292
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 57R56
zbMATH DE Number: 6078199
zbMATH Keywords: state-sum invariants
zbMATH Keywords: HQFT
zbMATH Keywords: TQFT
zbMATH Keywords: graded categories
zbMATH Keywords: fusion categories
MaRDI profile type: Publication
arXiv ID: 1202.6292
cites work: Invariants of piecewise-linear 3-manifolds
cites work: On fusion categories.
cites work: Invariants of three-dimensional manifolds
cites work: Q4693151
cites work: Algorithmic topology and classification of 3-manifolds
cites work: Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier.
cites work: State sum invariants of 3-manifolds and quantum \(6j\)-symbols
OpenAlex ID: W2962963288
title: On 3-dimensional homotopy quantum field theory. I.
review text: For a discrete group \(G\) and a spherical \(G\)-fusion category whose neutral component has invertible dimension (definition in Section 4.2), the paper under review constructs an HQFT invariant of homotopy classes of maps from a compact 3-manifold \((M,\partial M)\) to \(K(G,1)\) the Eilenberg-MacLane space of \(G\). For \(G=1\) these are the familiar Turaev-Viro TQFT invariants.NEWLINENEWLINEThe construction elegantly avoids the use of \(6j\)--symbols and allows non-generic skeletons of \(3\)--manifolds (skeletons with edges incident to \(\geq 4\) regions) in the spirit of [\textit{V. Turaev} and \textit{A. Virelizier}, ``On two approaches to 3-dimensional TQFTs'', \url{arXiv:1006.3501}].
reviewed by: Daniel Moskovich
description: scientific article; zbMATH DE number 6078199