Constructing convex projective 3-manifolds with generalized cusps

Abstract

We prove that non-compact finite volume hyperbolic 3-manifolds that satisfy a mild cohomological condition (infinitesimal rigidity) admit a family of properly convex deformations of their complete hyperbolic structure where the ends become generalized cusps of type 1 or type 2. We also discuss methods for controlling which types of cusp occur. Using these methods we produce the first known example of a 1-cusped hyperbolic 3-manifold that admits a convex projective structure with a type 2 cusp. We also use these techniques to produce new 1-cusped manifolds that admit a convex projective structure with a type 1 cusp.

arXiv commentv3 final version: fixed several typos, added section explaining the relevant obstruction theory. 33 pages comments welcome

References in corpus (8)

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Cited by in corpus (2)

• Generalized Cusps in Real Projective Manifolds: Classification
• Convex projective manifolds with a cusp of any non-diagonalizable type