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Actions of higher-rank lattices on free groups

Part of: Lie groups Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  29 July 2011

Martin R. Bridson  and
Richard D. Wade
Martin R. Bridson
Affiliation:
Mathematical Institute, 24–29 St Giles’, Oxford OX1 3LB, UK (email: bridson@maths.ox.ac.uk)
Richard D. Wade
Affiliation:
Mathematical Institute, 24–29 St Giles’, Oxford OX1 3LB, UK (email: wade@maths.ox.ac.uk)
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Abstract

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If G is a semisimple Lie group of real rank at least two and Γ is an irreducible lattice in G, then every homomorphism from Γ to the outer automorphism group of a finitely generated free group has finite image.

Keywords

automorphism groups of free groupshigher-rank latticessuperrigidity

MSC classification

Secondary: 20E36: Automorphisms of infinite groups 20F65: Geometric group theory 22E40: Discrete subgroups of Lie groups 20F14: Derived series, central series, and generalizations
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 5 , September 2011 , pp. 1573 - 1580
Copyright
Copyright © Foundation Compositio Mathematica 2011

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