Volume 22, issue 2 (2018)

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

Richard H Bamler

Geometry & Topology 22 (2018) 893–948
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.

Keywords
$3$–manifolds, simplicial complexes in $3$–manifolds, geometrization of $3$–manifolds, combinatorial geometry
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53C44, 57M15