Combinatorial Proofs in Bordered Heegaard Floer homology

TL;DR

This paper presents a combinatorial approach to proving invariance in bordered Heegaard Floer homology, simplifying the understanding of its algebraic structures and their topological invariance.

Contribution

It provides a new combinatorial construction and proof of invariance for the hat version of Heegaard Floer homology using bordered Floer theory.

Findings

Established combinatorial invariance of the hat version of Heegaard Floer homology.

Proved invariance of the linear-categorical representation of the mapping class groupoid.

Simplified the proof of invariance using combinatorial methods.

Abstract

Using bordered Floer theory, we give a combinatorial construction and proof of invariance for the hat version of Heegaard Floer homology. As a part of the proof, we also establish combinatorially the invariance of the linear-categorical representation of the strongly-based mapping class groupoid given by the same theory.