#### Volume 15, issue 4 (2011)

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Infinitesimal projective rigidity under Dehn filling

### Michael Heusener and Joan Porti

Geometry & Topology 15 (2011) 2017–2071
##### Abstract

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.

##### Keywords
projective structure, variety of representations, infinitesimal deformation
##### Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 53A20, 53C15