Contact structures, sutured Floer homology and TQFT

TL;DR

This paper develops a gluing map in sutured Floer homology induced by contact structures, leading to a (1+1)-dimensional TQFT via dimensional reduction, and explores its properties.

Contribution

It introduces a natural gluing map in sutured Floer homology associated with contact structures and constructs a new TQFT through dimensional reduction.

Findings

The gluing map respects the sutured Floer homology structure.

A (1+1)-dimensional TQFT is constructed from the gluing map.

Properties of the TQFT are analyzed in the context of contact topology.

Abstract

We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',\Gamma') into a larger sutured manifold (M,\Gamma), together with a contact structure on M-M'. As an application of this gluing map, we produce a (1+1)-dimensional TQFT by dimensional reduction and study its properties.