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
References
Publication
Received: 16 December 2014
Revised: 21 January 2016
Accepted: 21 January 2017
Published: 16 January 2018
Proposed: Tobias H. Colding
Seconded: Bruce Kleiner, Gang Tian
Authors
Richard H Bamler
Department of Mathematics
University of California
Berkeley, CA
United States
https://math.berkeley.edu/~rbamler/