#### Volume 22, issue 3 (2018)

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Convex projective structures on nonhyperbolic three-manifolds

### Samuel A Ballas, Jeffrey Danciger and Gye-Seon Lee

Geometry & Topology 22 (2018) 1593–1646
##### Abstract

Y Benoist proved that if a closed three-manifold $M$ admits an indecomposable convex real projective structure, then $M$ is topologically the union along tori and Klein bottles of finitely many submanifolds each of which admits a complete finite volume hyperbolic structure on its interior. We describe some initial results in the direction of a potential converse to Benoist’s theorem. We show that a cusped hyperbolic three-manifold may, under certain assumptions, be deformed to convex projective structures with totally geodesic torus boundary. Such structures may be convexly glued together whenever the geometry at the boundary matches up. In particular, we prove that many doubles of cusped hyperbolic three-manifolds admit convex projective structures.

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##### Keywords
real projective structures, three-manifolds, moduli spaces, representations of groups, divisible convex sets
##### Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 20H10, 53A20, 57M60, 57S30
##### Publication
Received: 26 September 2016
Revised: 21 August 2017
Accepted: 15 October 2017
Published: 16 March 2018
Proposed: Ian Agol
Seconded: Bruce Kleiner, Dmitri Burago
##### Authors
 Samuel A Ballas Department of Mathematics Florida State University Tallahassee, FL United States https://www.math.fsu.edu/~ballas/ Jeffrey Danciger Department of Mathematics The University of Texas Austin, TX United States https://www.ma.utexas.edu/users/jdanciger/ Gye-Seon Lee Mathematisches Institut Ruprecht-Karls-Universität Heidelberg Heidelberg Germany https://www.mathi.uni-heidelberg.de/~lee/