## Algebraic & Geometric Topology

### On deformations of hyperbolic 3–manifolds with geodesic boundary

Roberto Frigerio

#### Abstract

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

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

Dates
Accepted: 20 February 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796519

Digital Object Identifier
doi:10.2140/agt.2006.6.435

Mathematical Reviews number (MathSciNet)
MR2220684

Zentralblatt MATH identifier
1142.58016

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796519

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