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

Bamler, Richard

doi:10.2140/gt.2018.22.893

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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

DOI: 10.2140/gt.2018.22.893

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/

Volume 22, issue 2 (2018)