Remarks on 2-dimensional HQFTs
type: Item
instance of: scholarly article
title: Remarks on 2-dimensional HQFTs
zbMATH Open document ID: 1226.57043
author: Mihai D. Staic
author: Vladimir Turaev
published in: Algebraic \& Geometric Topology
publication date: 2010-07-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.1380
review text: An \(X\)-space \((M, f)\) consists of a closed oriented manifold \(M\) and a map \(f: M\to X\). The second author introduced the concept of \(X\)-Homotopy Quantum Field Theory (\(X\)-HQFT). A \(d\)-dimensional \(X\)-HQFT is basically a functor from the category of \(d\)-dimensional \(X\)-spaces and \(d+1\)-dimensional \(X\)-cobordisms to the category of vector spaces over a field. An \(X\)-HQFT reduces to a Topological Quantum Field Theory when the target space \(X\) is contractible. In the paper under review the authors define twisted Frobenius algebras (TF-algebras) and show that one can construct a TF-algebra from every 2-dimensional HQFT, unique up to coboundary equivalence. The authors expect that ``every TF-algebra can be realized by a 2-dimensional HQFT, which would yield a complete algebraic characterization of 2-dimensional HQFTs''. The last section computes the underlying TF-algebras of the cohomological 2-dimensional HQFTs.
reviewed by: Qi Chen
Mathematics Subject Classification ID: 57R56
zbMATH DE Number: 5731291
zbMATH Keywords: homotopy quantum field theory
zbMATH Keywords: twisted Frobenius algebra
zbMATH Keywords: topological quantum field theory
zbMATH Keywords: TQFT
MaRDI profile type: Publication
OpenAlex ID: W3103252219
arXiv ID: 0912.1380
cites work: Topological quantum field theories
cites work: REPRESENTATIONS OF THE HOMOTOPY SURFACE CATEGORY OF A SIMPLY CONNECTED SPACE
cites work: Determination of the Second Homology and Cohomology Groups of a Space by Means of Homotopy Invariants
cites work: Formal homotopy quantum field theories. I: Formal maps and crossed \(\mathcal{C}\)-algebras.
cites work: Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier.
DOI: 10.2140/AGT.2010.10.1367
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description: scientific article