Regenerating hyperbolic cone structures from Nil

Details Regenerating hyperbolic cone structures from Nil Regenerating hyperbolic cone structures from Nil

2002-12-20

arxiv.org/abs/math/0212298v1

Geom. Topol. 6(2002) 815-852

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper24.abs.html

Scientific paper

Let O be a three-dimensional Nil-orbifold, with branching locus a knot Sigma transverse to the Seifert fibration. We prove that O is the limit of hyperbolic cone manifolds with cone angle in (pi-epsilon, pi). We also study the space of Dehn filling parameters of O-Sigma. Surprisingly it is not diffeomorphic to the deformation space constructed from the variety of representations of O-Sigma. As a corollary of this, we find examples of spherical cone manifolds with singular set a knot that are not locally rigid. Those examples have large cone angles.

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