Discrete Groups in Geometry and Analysis
Volume 67 of the series Progress in Mathematics pp 48106
Deformation Spaces Associated to Compact Hyperbolic Manifolds
 Dennis JohnsonAffiliated withDepartment of Mathematics, University of California
 , John J. MillsonAffiliated withDepartment of Mathematics, University of California
Abstract
In this paper we take a first step toward understanding representations of cocompact lattices in SO(n,1) into arbitrary Lie groups by studying the deformations of rational representations — see Proposition 5.1 for a rather general existence result. This proposition has a number of algebraic applications. For example, we remark that such deformations show that the Margulis SuperRigidity Theorem, see [30], cannot be extended to the rank 1 case. We remark also that if Γ ⊂ SO(n,1) is one of the standard arithmetic examples described in Section 7 then Γ has a faithful representation ρ′ in SO(n+1), the Galois conjugate of the uniformization representation, and Proposition 5.1 may be used to deform the direct sum of ρ′ and the trivial representation in SO(n+2) thereby constructing nontrivial families of irreducible orthogonal representations of Γ. However, most of this paper is devoted to studying certain spaces of representations which are of interest in differential geometry in a sense which we now explain.
 Title
 Deformation Spaces Associated to Compact Hyperbolic Manifolds
 Book Title
 Discrete Groups in Geometry and Analysis
 Book Subtitle
 Papers in Honor of G.D. Mostow on His Sixtieth Birthday
 Pages
 pp 48106
 Copyright
 1987
 DOI
 10.1007/9781489966643_3
 Print ISBN
 9781489966667
 Online ISBN
 9781489966643
 Series Title
 Progress in Mathematics
 Series Volume
 67
 Series ISSN
 07431643
 Publisher
 Birkhäuser Boston
 Copyright Holder
 Springer Science+Business Media New York
 Additional Links
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 Editors

 Roger Howe ^{(1)}
 Editor Affiliations

 1. Department of Mathematics, Yale University
 Authors

 Dennis Johnson ^{(2)}
 John J. Millson ^{(2)}
 Author Affiliations

 2. Department of Mathematics, University of California, Los Angeles, CA, 90024, USA
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