Examples of unstabilized critical Heegaard surfaces

TL;DR

This paper demonstrates that the standard minimal genus Heegaard splitting of a product of a closed orientable surface and a circle is a critical Heegaard splitting, contributing to the understanding of Heegaard surface stability.

Contribution

It establishes that a specific well-known Heegaard splitting is critical, providing new insights into the stability properties of such splittings.

Findings

The standard minimal genus Heegaard splitting of (closed orientable surface)×S^1 is critical.

This splitting is unstabilized and critical.

Supports the classification of critical Heegaard splittings.

Abstract

We show that the standard minimal genus Heegaard splitting of (closed orientable surface)\times S^1 is a critical Heegaard splitting.