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Junior Topology
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Theodore Weisman, RLM 12.166: Non-hyperbolic strictly convex projective manifolds
Wednesday, February 05, 2020, 02:00pm - 03:00pm
In the 1980's Gromov and Thurston constructed examples of closed Riemannian 4-manifolds with everywhere negative sectional curvature that do not admit a hyperbolic structure (in contrast to the situation in dimension 3, where a hyperbolic structure can always be found for a negatively curved closed manifold). Kapovich showed that many of the Gromov-Thurston manifolds admit convex projective structures, giving a family of examples of strictly convex projective structures on manifolds which do not come from deformations of hyperbolic structures. In this talk, I'll describe the manifolds in the Gromov-Thurston construction, say why they don't admit hyperbolic structures, and explain how Kapovich uses bending deformations to find projective structures on them.
Location: RLM 12.166

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