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November 2005 Local rigidity of 3-dimensional cone-manifolds
Hartmut Weiss
J. Differential Geom. 71(3): 437-506 (November 2005). DOI: 10.4310/jdg/1143571990

Abstract

We study the local deformation space of 3-dimensional cone-manifold structures of constant curvature κ is an element of {.1, 0, 1} and cone-angles ≤ π. Under this assumption on the cone-angles the singular locus will be a trivalent graph. In the hyperbolic and the spherical case our main result is a vanishing theorem for the first L2-cohomology group of the smooth part of the cone-manifold with coefficients in the flat bundle of infinitesimal isometries. We conclude local rigidity from this. In the Euclidean case we prove that the first L2-cohomology group of the smooth part with coefficients in the flat tangent bundle is represented by parallel forms.

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Hartmut Weiss. "Local rigidity of 3-dimensional cone-manifolds." J. Differential Geom. 71 (3) 437 - 506, November 2005. https://doi.org/10.4310/jdg/1143571990

Information

Published: November 2005
First available in Project Euclid: 28 March 2006

zbMATH: 1098.53038
MathSciNet: MR2198808
Digital Object Identifier: 10.4310/jdg/1143571990

Rights: Copyright © 2005 Lehigh University

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Vol.71 • No. 3 • November 2005
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