Homotopy quantum field theories and tortile structures

2001/11/07 by M. Brightwell, P. Turner, Brightwell, M. +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.math/0111084

22 pages, with minor corrections

arxiv created 2002/03/13 · arxiv updated 2009/11/30

Abstract

We study a variation of Turaev's homotopy quantum field theories using 2-categories of surfaces. We define the homotopy surface 2-category of a space X and define an \cS_X-structure to be a monoidal 2-functor from this to the 2-category of idempotent-complete additive k-linear categories. We initiate the study of the algebraic structure arising from these functors. In particular we show that, under certain conditions, an \cS_X-structure gives rise to a lax tortile π-category when the background space is an Eilenberg-Maclane space X=K(π,1), and to a tortile category with lax π₂X-action when the background space is simply-connected.

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