Infinitesimal projective rigidity under Dehn filling

Heusener, Michael¹ ; Porti, Joan²

¹ Laboratoire de Mathématiques, UMR 6620 - CNRS, Université Blaise Pascal, BP 80026, F-63171 Aubiere, France
² Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

Geometry & topology, Tome 15 (2011) no. 4, pp. 2017-2071.

Résumé

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 $M$ is infinitesimally projectively rigid relative to the cusps, then infinitely many hyperbolic Dehn fillings on $M$ 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.

Détail

DOI : 10.2140/gt.2011.15.2017

Keywords: projective structure, variety of representations, infinitesimal deformation

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