Combinatorial knot Floer homology and cyclic double branched covers

TL;DR

This paper presents a combinatorial proof of the invariance of knot Floer homology over integers for cyclic double branched covers of knots, utilizing Heegaard diagrams to analyze the pullback of knots.

Contribution

It introduces a combinatorial approach to prove the invariance of knot Floer homology in cyclic double branched covers, expanding computational techniques.

Findings

Provides a combinatorial proof of invariance over Z

Uses Heegaard diagrams for pullback knots

Enhances understanding of knot Floer homology in branched covers

Abstract

Using a Heegaard diagram for the pullback of a knot $K \subset S^3$ in its cyclic double branched cover $\Sigma_2(K)$, we give a combinatorial proof for the invariance of knot Floer homology over $\mathbb{Z}$.