Heegaard diagrams corresponding to Turaev surfaces

TL;DR

This paper establishes a correspondence between Turaev surfaces of link diagrams on the sphere and special Heegaard diagrams for the 3-sphere that are adapted to links, providing a new perspective on link invariants.

Contribution

It introduces a novel correspondence linking Turaev surfaces and special Heegaard diagrams for links in the 3-sphere.

Findings

New correspondence between Turaev surfaces and Heegaard diagrams

Enhanced understanding of link invariants via this correspondence

Potential applications to link and 3-manifold topology

Abstract

We describe a correspondence between Turaev surfaces of link diagrams on $S^2\subset S^3$ and special Heegaard diagrams for $S^3$ adapted to links.