Regenerating hyperbolic cone structures from Nil

Let $O$ be a three-dimensional $N i l$ –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

References

Forward citations

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

Volume 6, issue 2 (2002)

Joan Porti