## Geometry & Topology

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

Hartmut Weiß

#### Abstract

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

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

Dates
Accepted: 9 September 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732526

Digital Object Identifier
doi:10.2140/gt.2013.17.329

Mathematical Reviews number (MathSciNet)
MR3035330

Zentralblatt MATH identifier
1262.53032

#### Citation

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. https://projecteuclid.org/euclid.gt/1513732526

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