Volume 11, issue 3 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Deforming Euclidean cone 3–manifolds

Joan Porti and Hartmut Weiß

Geometry & Topology 11 (2007) 1507–1538

arXiv: math.GT/0510432

Abstract

Given a closed orientable Euclidean cone 3–manifold C with cone angles 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/