Formal Homotopy Quantum Field Theories, I: Formal Maps and Crossed C-algebras

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dc.creatorPorter, Timothy
dc.creatorTuraev, Vladimir
dc.date2005-12-01
dc.date2008-02-11
dc.date.accessioned2026-07-07T09:19:40Z
dc.date.available2026-07-07T09:19:40Z
dc.descriptionHomotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed $d$-manifolds endowed with extra structure in the form of homotopy classes of maps into a given `target' space, $B$. For $d = 1$, classifications of HQFTs in terms of algebraic structures are known when $B$ is a $K(G,1)$ and also when it is simply connected. Here we study general HQFTs with $d = 1$ and target a general 2-type, giving a common generalisation of the classifying algebraic structures for the two cases previously known. The algebraic models for 2-types that we use are crossed modules, $\mathcal{C}$, and we introduce a notion of formal $\mathcal{C}$-map, which extends the usual lattice-type constructions to this setting. This leads to a classification of `formal' 2-dimensional HQFTs with target $\mathcal{C}$, in terms of crossed $\mathcal{C}$-algebras.
dc.description37 pages, version 2 with some restructuring and correction of minor typos etc
dc.identifierhttps://arxiv.org/abs/math/0512032
dc.identifierhttp://arxiv.org/abs/math/0512032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154474
dc.subjectQuantum Algebra
dc.subject18G50; 55P99
dc.titleFormal Homotopy Quantum Field Theories, I: Formal Maps and Crossed C-algebras
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