Geometry & Topology, Vol. 6 (2002) Paper no. 24, pages 815--852.

Regenerating hyperbolic cone structures from Nil

Joan Porti

Abstract. 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.

Keywords. Hyperbolic structure, cone 3--manifolds, local rigidity

AMS subject classification. Primary: 57M10. Secondary: 58M15.

DOI: 10.2140/gt.2002.6.815

E-print: arXiv:math.GT/0212298

Submitted to GT on 16 July 2001. (Revised 9 December 2002.) Paper accepted 18 December 2002. Paper published 18 December 2002.

Notes on file formats

Joan Porti
Departament de Matematiques, Universitat Autonoma de Barcelona
08193 Bellaterra, Spain

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