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Infinitesimal projective
rigidity under Dehn filling
Michael Heusener and Joan Porti |
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Geometry & Topology 15 (2011) 2017–2071
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Abstract |
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To a hyperbolic manifold one can associate a canonical projective structure and a fundamental question is whether or not it can be deformed. In particular, the canonical projective structure of a finite volume hyperbolic manifold with cusps might have deformations which are trivial on the cusps. The aim of this article is to prove that if the canonical projective structure on a cusped hyperbolic manifold is infinitesimally projectively rigid relative to the cusps, then infinitely many hyperbolic Dehn fillings on are locally projectively rigid. We analyze in more detail the figure eight knot and the Whitehead link exteriors, for which we can give explicit infinite families of slopes with projectively rigid Dehn fillings. |
Keywords
projective structure, variety of representations,
infinitesimal deformation
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Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 53A20, 53C15
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References |
Publication
Received: 8 May 2010
Revised: 10 August 2011
Accepted: 13 September 2011
Published: 23 October 2011
Proposed: Walter Neumann
Seconded: David Gabai, Jean-Pierre Otal
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Authors |
| Michael Heusener | |
| Laboratoire de Mathématiques, UMR
6620 - CNRS Université Blaise Pascal BP 80026 F-63171 Aubiere France |
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| http://math.univ-bpclermont.fr/~heusener/ | |
| Joan Porti | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona 08193 Bellaterra Spain |
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| http://mat.uab.es/~porti/ | |
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