Link cobordisms and functoriality in link Floer homology

TL;DR

This paper develops cobordism maps for link Floer homology associated with decorated link cobordisms, establishing their invariance and comparing with the graph TQFT in Heegaard Floer theory.

Contribution

It introduces a new construction of cobordism maps on link Floer homology and proves their invariance, enhancing the functorial framework of the theory.

Findings

Constructed cobordism maps on link Floer homology.

Proved invariance of the cobordism maps.

Compared with the graph TQFT for Heegaard Floer homology.

Abstract

We construct cobordism maps on link Floer homology associated to decorated link cobordisms. The maps are defined on a curved chain homotopy type invariant. We describe the construction, and prove invariance. We also make a comparison with the graph TQFT for Heegaard Floer homology.