Critical Heegaard surfaces obtained by self-amalgamation

TL;DR

This paper investigates conditions under which self-amalgamated Heegaard surfaces are critical, contributing to the understanding of topological index 2 minimal surfaces in 3-manifold topology.

Contribution

It provides both necessary and sufficient conditions for self-amalgamated Heegaard surfaces to be critical, advancing the theory of critical surfaces.

Findings

Identifies sufficient conditions for criticality.

Establishes necessary conditions for criticality.

Enhances understanding of topological index 2 minimal surfaces.

Abstract

Critical surfaces can be regarded as topological index 2 minimal surfaces which was introduced by David Bachman. In this paper we give a sufficient condition and a necessary condition for self-amalgamated Heegaard surfaces to be critical.