Infinitesimal projective rigidity under Dehn filling

Michael Heusener, Joan Porti

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)2017-2071
JournalGeometry and Topology
Volume15
Issue number4
DOIs
Publication statusPublished - 12 Dec 2011

Keywords

  • Infinitesimal deformation
  • Projective structure
  • Variety of representations

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