Geometry & Topology

The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$

Hartmut Weiß

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We develop the deformation theory of hyperbolic cone–3–manifolds with cone-angles less than 2π, that is, contained in the interval (0,2π). In the present paper we focus on deformations keeping the topological type of the cone-manifold fixed. We prove local rigidity for such structures. This gives a positive answer to a question of A Casson.

Article information

Geom. Topol., Volume 17, Number 1 (2013), 329-367.

Received: 12 April 2012
Accepted: 9 September 2012
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 57M50: Geometric structures on low-dimensional manifolds

cone-manifolds geometric structures on low-dimensional manifolds hyperbolic geometry


Weiß, Hartmut. The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$. Geom. Topol. 17 (2013), no. 1, 329--367. doi:10.2140/gt.2013.17.329.

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