Stable equivalence of handlebody decompositions whose partitions are multibranched surfaces

TL;DR

This paper investigates the stable equivalence of handlebody decompositions of 3-manifolds with multibranched surface intersections, introducing stabilization operations to establish equivalence.

Contribution

It defines stabilization operations for handlebody decompositions with multibranched surface intersections and proves their stable equivalence.

Findings

Stabilization operations ensure stable equivalence of decompositions.

Handles with multibranched surface intersections can be stabilized.

The approach generalizes previous handlebody decomposition theories.

Abstract

In this paper, we consider decompositions of closed orientable 3-manifolds with more than 3 handlebodies, where the union of intersections of handlebodies is a multibranched surface. We define stabilization operations for such decompositions and show the stable equivalence.