Convex projective structures on Gromov-Thurston manifolds

By Michael Kapovich. 2006

70 citations recorded by the source corpus.

We consider Gromov–Thurston examples of negatively curved n-manifolds which do not admit metrics of constant sectional curvature. We show that for each n ≥ 4 some of the Gromov–Thurston manifolds admit strictly convex real–projective structures.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e3955ac5735170535addc01adf6b7dd4b788d05

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. J. Danciger
2. Anna Wienhard
3. Darren D. Long
4. Olivier Y Guichard

In Geometry and Topology

1. Anna Wienhard
2. J. Danciger
3. Olivier Y Guichard
4. Gye-Seon Lee
5. Samuel A. Ballas
6. Stephan Tillmann
7. Darren D. Long
8. Daryl Cooper

In Mathematical Physics

1. Anna Wienhard
2. Olivier Y Guichard
3. J. Danciger
4. Gye-Seon Lee
5. Samuel A. Ballas
6. Andr'es Sambarino
7. Michael Kapovich
8. B. Leeb

Citations in the corpus

• On Convex Projective Manifolds and Cusps (2011, background): “However, projective manifolds are more general: Kapovich [36] has shown that there are closed strictly convex 4–manifolds which do not admit a hyperbolic structure.”
• Convex projective structures on nonhyperbolic three-manifolds (2015, background): “It follows easily from Calabi–Weil rigidity [8, 40, 41] (or see Kapovich [29]) that the PSL2C traces of resiρt become complex to first order.”
• Anosov representations: domains of discontinuity and applications (2011, background): “Kapovich [48] provides several examples of convex real projective structures on Gromov-Thurston manifolds, i.”
• Around groups in Hilbert Geometry (2013, unknown): “11 (Benoist d = 4 [11], Kapovich d > 4 [48]).”