Decompositions of the 3-sphere and lens spaces with three handlebodies

Abstract

In this paper, we consider decompositions of 3-manifolds with three handlebodies. We classify such decompositions of the 3-sphere and lens spaces with small genera. These decompositions admit operations called stabilizations. We also determine whether these decompositions are obtained by stabilization from another decomposition.

Stable equivalence of handlebody decompositions whose partitions are multibranched surfaces

“…Recently, we introduced a handlebody decomposition of a closed orientable 3manifold [10,8]. If a 3-manifold is decomposed into several handlebodies, then we call this decomposition a handlebody decomposition.…”