Continuity of discrete homomorphisms of diffeomorphism groups

Hurtado, Sebastian

doi:10.2140/gt.2015.19.2117

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Continuity of discrete homomorphisms of diffeomorphism groups

Sebastian Hurtado

Geometry & Topology 19 (2015) 2117–2154

DOI: 10.2140/gt.2015.19.2117

Abstract

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

Keywords

example, sample layout

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

Volume 19, issue 4 (2015)