Volume 12, issue 1 (2008)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Quakebend deformations in complex hyperbolic quasi-Fuchsian space

Ioannis D Platis

Geometry & Topology 12 (2008) 431–459
Abstract

We study quakebend deformations in complex hyperbolic quasi-Fuchsian space Q(Σ) of a closed surface Σ of genus g > 1, that is the space of discrete, faithful, totally loxodromic and geometrically finite representations of the fundamental group of Σ into the group of isometries of complex hyperbolic space. Emanating from an –Fuchsian point ρ Q(Σ), we construct curves associated to complex hyperbolic quakebending of ρ and we prove that we may always find an open neighborhood U(ρ) of ρ in Q(Σ) containing pieces of such curves. Moreover, we present generalisations of the well known Wolpert–Kerckhoff formulae for the derivatives of geodesic length function in Teichmüller space.

Keywords
complex hyperbolic, bending
Mathematical Subject Classification 2000
Primary: 32G05
Secondary: 32M05
References
Publication
Received: 23 February 2007
Accepted: 6 December 2007
Published: 12 March 2008
Proposed: Jean-Pierre Otal
Seconded: Walter Neumann, Benson Farb
Authors
Ioannis D Platis
Department of Mathematics
Aristotle University of Salonica
Salonica
Greece
http://www.math.uoc.gr/~jplatis/