Deforming Euclidean cone 3–manifolds

Porti, Joan; Weiß, Hartmut

doi:10.2140/gt.2007.11.1507

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Deforming Euclidean cone 3–manifolds

Joan Porti and Hartmut Weiß

Geometry & Topology 11 (2007) 1507–1538

DOI: 10.2140/gt.2007.11.1507

arXiv: math.GT/0510432

Abstract

Given a closed orientable Euclidean cone 3–manifold $C$ with cone angles $\leq π$ and which is not almost product, we describe the space of constant curvature cone structures on $C$ with cone angles $< π$ . We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbolic ones and we also deduce global rigidity for Euclidean cone structures.

Keywords

cone 3–manifold, deformation space

Mathematical Subject Classification 2000

Primary: 57M50

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Publication

Received: 21 October 2005

Revised: 7 June 2007

Accepted: 11 May 2007

Published: 23 July 2007

Proposed: Jean-Pierre Otal

Seconded: Martin Bridson, Walter Neumann

Authors

Joan Porti
Departament de Matemàtiques Universitat Autònoma de Barcelona E-08193 Bellaterra Spain
http://mat.uab.es/~porti/
Hartmut Weiß
Mathematisches Institut Universität München Theresienstraße 39 D-80333 München Germany
http://www.mathematik.uni-muenchen.de/~weiss/

Volume 11, issue 3 (2007)