Geometry & Topology

Flexing closed hyperbolic manifolds

Daryl Cooper, Darren Long, and Morwen Thistlethwaite

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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.

Article information

Source
Geom. Topol., Volume 11, Number 4 (2007), 2413-2440.

Dates
Received: 18 December 2006
Accepted: 3 September 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799985

Digital Object Identifier
doi:10.2140/gt.2007.11.2413

Mathematical Reviews number (MathSciNet)
MR2372851

Zentralblatt MATH identifier
1142.57009

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

Keywords
real projective structure complex isometry flexing

Citation

Cooper, Daryl; Long, Darren; Thistlethwaite, Morwen. Flexing closed hyperbolic manifolds. Geom. Topol. 11 (2007), no. 4, 2413--2440. doi:10.2140/gt.2007.11.2413. https://projecteuclid.org/euclid.gt/1513799985


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