Algebraic & Geometric Topology

On deformations of hyperbolic 3–manifolds with geodesic boundary

Roberto Frigerio

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Let M be a complete finite-volume hyperbolic 3–manifold with compact non-empty geodesic boundary and k toric cusps, and let T be a geometric partially truncated triangulation of M. We show that the variety of solutions of consistency equations for T is a smooth manifold or real dimension 2k near the point representing the unique complete structure on M. As a consequence, the relation between deformations of triangulations and deformations of representations is completely understood, at least in a neighbourhood of the complete structure. This allows us to prove, for example, that small deformations of the complete triangulation affect the compact tetrahedra and the hyperbolic structure on the geodesic boundary only at the second order.

Article information

Algebr. Geom. Topol., Volume 6, Number 1 (2006), 435-457.

Received: 7 October 2005
Accepted: 20 February 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58H15: Deformations of structures [See also 32Gxx, 58J10]
Secondary: 57M50: Geometric structures on low-dimensional manifolds 20G10: Cohomology theory

geodesic triangulation truncated tetrahedron cohomology of representations


Frigerio, Roberto. On deformations of hyperbolic 3–manifolds with geodesic boundary. Algebr. Geom. Topol. 6 (2006), no. 1, 435--457. doi:10.2140/agt.2006.6.435.

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