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2018 Convex projective structures on nonhyperbolic three-manifolds
Samuel A Ballas, Jeffrey Danciger, Gye-Seon Lee
Geom. Topol. 22(3): 1593-1646 (2018). DOI: 10.2140/gt.2018.22.1593

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.

Citation

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Samuel A Ballas. Jeffrey Danciger. Gye-Seon Lee. "Convex projective structures on nonhyperbolic three-manifolds." Geom. Topol. 22 (3) 1593 - 1646, 2018. https://doi.org/10.2140/gt.2018.22.1593

Information

Received: 26 September 2016; Revised: 21 August 2017; Accepted: 15 October 2017; Published: 2018
First available in Project Euclid: 31 March 2018

zbMATH: 06864264
MathSciNet: MR3780442
Digital Object Identifier: 10.2140/gt.2018.22.1593

Subjects:
Primary: 57M50
Secondary: 20H10, 53A20, 57M60, 57S30

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.22 • No. 3 • 2018
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