Sutured Floer homology, sutured TQFT and noncommutative QFT

摘要

We define a "sutured topological quantum field theory", motivated by the studyof sutured Floer homology of product 3—manifolds, and contact elements. Westudy a rich algebraic structure of suture elements in sutured TQFT, showing that itcorresponds to contact elements in sutured Floer homology. We use this approach tomake computations of contact elements in sutured Floer homology over Z of suturedmanifolds (D~2x S~1, Fx 1)whereFis finite. This generalises previous resultsof the author over Z_2coefficients. Our approach elaborates upon the quantum fieldtheoretic aspects of sutured Floer homology, building a noncommutative Fock space,together with a bilinear form deriving from a certain combinatorial partial order; weshow that the sutured TQFT of discs is isomorphic to this Fock space.