On topologically minimal surfaces of high genus

TL;DR

This paper demonstrates that 3-manifolds with incompressible surfaces can contain topologically minimal surfaces of any high genus, expanding understanding of surface complexity within such manifolds.

Contribution

It establishes the existence of topologically minimal surfaces of arbitrarily high genus in 3-manifolds containing incompressible surfaces, a new result in 3-manifold topology.

Findings

Existence of high genus topologically minimal surfaces

Incompressible surfaces imply complex minimal surface structures

High genus surfaces can be constructed within certain 3-manifolds

Abstract

We show that a 3-manifold containing an incompressible surface has topologically minimal surfaces of arbitrary high genus.