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Complex twist flows on
surface group representations and the local shape of the
deformation space of hyperbolic cone–$3$–manifolds
Grégoire Montcouquiol and Hartmut Weiß |
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Geometry & Topology 17 (2013) 369–412
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Abstract |
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In the former articles [arXiv:0903.4743 and this volume pp 329-367], it was independently proven by the authors that the space of hyperbolic cone––manifolds with cone angles less than and fixed singular locus is locally parametrized by the cone angles. In this sequel, we investigate the local shape of the deformation space when the singular locus is no longer fixed, ie when the singular vertices can be split. We show that the different possible splittings correspond to specific pair-of-pants decompositions of the smooth parts of the links of the singular vertices, and that under suitable assumptions the corresponding subspace of deformations is parametrized by the cone angles of the original edges and the lengths of the new ones. |
Keywords
Cone-manifolds, surface group representations, hyperbolic
geometry
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Mathematical Subject Classification 2010
Primary: 57M50, 58D27
Secondary: 53C35
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References |
Publication
Received: 3 May 2011
Revised: 2 May 2012
Accepted: 6 September 2012
Published: 11 March 2013
Proposed: Jean-Pierre Otal
Seconded: Simon Donaldson, David Gabai
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Authors |
| Grégoire Montcouquiol | |
| Univ. Paris-Sud, Laboratoire de
Mathématiques UMR8628 CNRS Orsay F-91405 France |
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| http://www.math.u-psud.fr/~montcouq/ | |
| Hartmut Weiß | |
| LMU München Mathematisches Institut Theresienstr. 39 D-80333 München Germany |
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| http://www.mathematik.uni-muenchen.de/~weiss/ | |
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