Volume 22, issue 2 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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/