Each Thurston geometry admits a Heegaard genus two example

TL;DR

This paper provides explicit genus two Heegaard diagrams for compact 3-manifolds across all eight Thurston geometries, enriching the understanding of their topological structures.

Contribution

It systematically constructs genus two Heegaard diagrams for manifolds with each Thurston geometry, offering new explicit examples.

Findings

Explicit genus two diagrams for all Thurston geometries

Enhanced understanding of 3-manifold topologies

Foundation for further geometric topology research

Abstract

We collect examples of genus two Heegaard diagrams for compact 3-manifolds admitting each of the eight Thurston geometries.