A Heegaard-Floer TQFT for link cobordisms

TL;DR

This paper constructs a new Heegaard-Floer homology TQFT for links in 3-manifolds and surface cobordisms in 4-manifolds, which is decoration-independent and explores its fundamental properties.

Contribution

It introduces a novel, decoration-independent Heegaard-Floer TQFT for links and cobordisms, expanding the framework of link invariants in 3- and 4-manifolds.

Findings

Defines a functor from links and cobordisms to $\\mathbb{F}[v]$-modules

Establishes basic properties of the TQFT

Demonstrates independence from link decoration

Abstract

We introduce a Heegaard-Floer homology functor from the category of oriented links in closed $3$-manifolds and oriented surface cobordisms in $4$-manifolds connecting them to the category of $\mathbb{F}[v]$-modules and $\mathbb{F}[v]$-homomorphisms between them, where $\mathbb{F}$ is the field with two elements. In comparison with previously defined TQFTs for decorated links and link cobordisms, the construction of this paper has the advantage of being independent from the decoration. Some of the basic properties of this functor are also explored.