Volume 11, issue 4 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Flexing closed hyperbolic manifolds

D Cooper, D D Long and M B Thistlethwaite

Geometry & Topology 11 (2007) 2413–2440
Abstract

We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the presence of a mild smoothness hypothesis, the existence of such real projective deformations is equivalent to the question of whether one can nontrivially deform the canonical representation of the real hyperbolic structure when it is considered as a group of complex hyperbolic isometries. The set of closed hyperbolic manifolds for which one can do this seems mysterious.

Keywords
real projective structure, complex isometry, flexing
Mathematical Subject Classification 2000
Primary: 57M50
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Publication
Received: 18 December 2006
Accepted: 3 September 2007
Published: 17 December 2007
Proposed: Walter Neumann
Seconded: Dave Gabai, Martin Bridson
Authors
D Cooper
Department of Mathematics
University of California
Santa Barbara CA 93106
USA
D D Long
Department of Mathematics
University of California
Santa Barbara CA 93106
USA
M B Thistlethwaite
Department of Mathematics
University of Tennessee
Knoxville TN 37996
USA