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Regenerating hyperbolic cone structures from Nil

Joan Porti

Geometry & Topology 6 (2002) 815–852

arXiv: math.GT/0212298

Abstract

Let O be a three-dimensional Nil–orbifold, with branching locus a knot Σ transverse to the Seifert fibration. We prove that O is the limit of hyperbolic cone manifolds with cone angle in (π ε,π). We also study the space of Dehn filling parameters of O Σ. Surprisingly it is not diffeomorphic to the deformation space constructed from the variety of representations of O Σ. 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.

Keywords
Hyperbolic structure, cone 3–manifolds, local rigidity
Mathematical Subject Classification 2000
Primary: 57M10
Secondary: 58M15
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Publication
Received: 16 July 2001
Revised: 9 December 2002
Accepted: 18 December 2002
Published: 18 December 2002
Proposed: Jean-Pierre Otal
Seconded: David Gabai, Walter Neumann
Authors
Joan Porti
Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Bellaterra
Spain