On two types of Heegaard diagram used in knot Floer homology

TL;DR

This paper demonstrates how to explicitly transform between different local and global Heegaard diagrams used in knot Floer homology through a sequence of Heegaard moves, clarifying their interrelations.

Contribution

It provides an explicit sequence of Heegaard moves connecting local and global diagrams in knot Floer homology, enhancing understanding of their equivalence.

Findings

Explicit sequence of Heegaard moves between diagram types

Connection between local and global Heegaard diagrams

Clarification of diagram transformations in knot Floer homology

Abstract

In this brief note, we give an explicit sequence of Heegaard moves interpolating between local versions of the Kauffman-states Heegaard diagram and the planar Heegaard diagram used in knot Floer homology, and show how these local moves can be used to go between the global versions of the Heegaard diagrams.