Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors

TL;DR

This paper classifies essential surfaces with non-negative Euler characteristic within genus two handlebody exteriors embedded in the 3-sphere, advancing understanding of their topological structure.

Contribution

It offers a comprehensive classification of such surfaces, a novel contribution to the study of 3-manifold topology and handlebody exteriors.

Findings

Complete classification of essential surfaces with non-negative Euler characteristic

Identification of key topological features of genus two handlebody exteriors

Insights into the structure of embedded handlebodies in the 3-sphere

Abstract

We provide a classification of the essential surfaces of non-negative Euler characteristic in the exteriors of genus two handlebodies embedded in the 3-sphere.