#### 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

Email: porti@mat.uab.es

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