Long-time behavior of $3$–dimensional Ricci flow, C: $3$–manifold topology and combinatorics of simplicial complexes in $3$–manifolds

Abstract

In the third part of this series of papers, we establish several topological results that will become important for studying the long-time behavior of Ricci flows with surgery. In the first part of this paper we recall some elementary observations in the topology of $3$–manifolds. The main part is devoted to the construction of certain simplicial complexes in a given $3$–manifold that exhibit useful intersection properties with embedded, incompressible solid tori.

This paper is purely topological in nature and Ricci flows will not be used.