Convex projective structures on nonhyperbolic three-manifolds

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.

SEEK ID: https://publications.h-its.org/publications/984

DOI: 10.2140/gt.2018.22.1593

Research Groups: Groups and Geometry

Publication type: Journal

Journal: Geom. Topol.

Citation: Geom. Topol. 22(3):1593-1646

Date Published: 2018

URL: https://msp.org/gt/2018/22-3/p08.xhtml

Registered Mode: imported from a bibtex file

Authors: Samuel Ballas, Jeffrey Danciger, Gye-Seon Lee

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Citation
Ballas, S., Danciger, J., & Lee, G.-S. (2018). Convex projective structures on nonhyperbolic three-manifolds. In Geometry & Topology (Vol. 22, Issue 3, pp. 1593–1646). Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2018.22.1593
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Created: 30th Jan 2020 at 10:15

Last updated: 5th Mar 2024 at 21:24

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