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Geometry & Topology 11 (2007) 24132440 2413 Flexing closed hyperbolic manifolds.
 

Summary: Geometry & Topology 11 (2007) 24132440 2413
Flexing closed hyperbolic manifolds.
D COOPER
D D LONG
M B THISTLETHWAITE
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.
57M50
1 Introduction
As remarked by Schwartz [20], it is a basic problem to understand how discrete
faithful representations W ! G0 can be deformed if we extend the Lie group
G0 to a larger Lie group G1 . The best understood example of this is the case of
quasifuchsian deformation, where is the fundamental group of a closed orientable
surface and the Lie group pair .G0; G1/ is .PSL.2; /; PSL.2; //. However, there has
been an enormous amount of interesting work, we mention the exploration of bending

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics