On the annulus complex of a handlebody

TL;DR

This paper introduces the annulus complex of a handlebody, providing a formal definition and demonstrating its connectivity using combinatorial methods, contributing to the understanding of handlebody topology.

Contribution

The paper defines the annulus complex of a handlebody and proves its connectivity through combinatorial techniques, a novel approach in this area.

Findings

Annulus complex is connected.

Combinatorial methods effectively prove connectivity.

Provides foundational understanding for handlebody topology.

Abstract

In this paper, we give the definition of the annulus complex of a handlebody and use the combinatorial methods to prove its connectivity.