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

摘要

In the third part of this series of papers, we establish several topologicalresults that will become important for studying the long-time behavior of Ricciflows with surgery. In the first part of this paper we recall some elementaryobservations in the topology of 3-manifolds. The main part is devoted to theconstruction of certain simplicial complexes in a given 3-manifold that exhibituseful intersection properties with embedded, incompressible solid tori. Thispaper is purely topological in nature and Ricci flows will not be used.