#### Volume 6, issue 2 (2002)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Regenerating hyperbolic cone structures from Nil

### Joan Porti

Geometry & Topology 6 (2002) 815–852
 arXiv: math.GT/0212298
##### Abstract

Let $\mathsc{O}$ be a three-dimensional $Nil$–orbifold, with branching locus a knot $\Sigma$ transverse to the Seifert fibration. We prove that $\mathsc{O}$ is the limit of hyperbolic cone manifolds with cone angle in $\left(\pi -\epsilon ,\pi \right)$. We also study the space of Dehn filling parameters of $\mathsc{O}-\Sigma$. Surprisingly it is not diffeomorphic to the deformation space constructed from the variety of representations of $\mathsc{O}-\Sigma$. 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
Primary: 57M10
Secondary: 58M15