Heegaard Floer homology as morphism spaces

TL;DR

This paper introduces a new pairing theorem for bordered Floer homology expressed via homomorphisms, aligning it more closely with TQFT frameworks and enabling new dualities.

Contribution

It presents a novel homomorphism-based pairing theorem for bordered Floer homology, enhancing conceptual connections with TQFT and Fukaya categories.

Findings

New homomorphism-based pairing theorem established

Enhanced compatibility with TQFT frameworks

Derived dualities in bordered Floer homology

Abstract

In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present formulation is closer in spirit to the usual TQFT framework, and allows a more direct comparison with Fukaya-categorical constructions. The result also leads to various dualities in bordered Floer homology.