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# Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

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1435-5345
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Volume 2017, Issue 725

# The long-time behavior of 3-dimensional Ricci flow on certain topologies

Richard H. Bamler
Published Online: 2014-11-12 | DOI: https://doi.org/10.1515/crelle-2014-0101

## Abstract

In this paper we analyze the long-time behavior of 3-dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric decomposition, there are only finitely many surgeries and the curvature is bounded by C ${t}^{-1}$ for large t. This proves a conjecture of Perelman for this class of initial topologies. The proof of this fact illustrates the fundamental ideas that are used in the subsequent papers of the author.

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Revised: 2014-06-23

Published Online: 2014-11-12

Published in Print: 2017-04-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2017, Issue 725, Pages 183–215, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102,

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