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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Continuity of discrete homomorphisms of diffeomorphism groups

Sebastian Hurtado

Geometry & Topology 19 (2015) 2117–2154
Abstract

Let M and N be two closed C manifolds and let Diffc(M) denote the group of C diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between Diffc(M) and Diffc(N) is continuous. We also show that a nontrivial group homomorphism Φ: Diffc(M) Diffc(N) implies that dim(M) dim(N) and give a classification of such homomorphisms when dim(M) = dim(N).

Keywords
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Mathematical Subject Classification 2010
Primary: 57M99
Secondary: 55Q33, 55Q32
References
Publication
Received: 13 September 2013
Revised: 4 August 2014
Accepted: 19 September 2014
Published: 29 July 2015
Proposed: Danny Calegari
Seconded: Benson Farb, Leonid Polterovich
Authors
Sebastian Hurtado
Department of Mathematics
University of California
Berkeley, CA 94720
USA