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2006 On deformations of hyperbolic 3–manifolds with geodesic boundary
Roberto Frigerio
Algebr. Geom. Topol. 6(1): 435-457 (2006). DOI: 10.2140/agt.2006.6.435


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.


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Roberto Frigerio. "On deformations of hyperbolic 3–manifolds with geodesic boundary." Algebr. Geom. Topol. 6 (1) 435 - 457, 2006.


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

zbMATH: 1142.58016
MathSciNet: MR2220684
Digital Object Identifier: 10.2140/agt.2006.6.435

Primary: 58H15
Secondary: 20G10, 57M50

Rights: Copyright © 2006 Mathematical Sciences Publishers


Vol.6 • No. 1 • 2006
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