2012/09/30 by Evan Fink, Fink, Evan
Computer Science · Mathematics · #Geometric and Algebraic Topology #Logic, programming, and type systems #math.GT #math.SG #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1210.0238
arxiv created 2012/09/30 · arxiv updated 2012/10/02
The idea of a sutured topological quantum field theory was introduced by Honda, Kazez and Matić (2008). A sutured TQFT associates a group to each sutured surface and an element of this group to each dividing set on this surface. The notion was originally introduced to talk about contact invariants in Sutured Floer Homology. We provide an elementary example of a sutured TQFT, which comes from taking exterior algebras of certain singular homology groups. We show that this sutured TQFT coincides with that of Honda et al. using \Z2-coefficients. The groups in our theory, being exterior algebras, naturally come with the structure of a ring with unit. We give an application of this ring structure to understanding tight contact structures on solid tori.