2:00 pm Wednesday, February 5, 2020
Junior Topology: Non-hyperbolic strictly convex projective manifolds by Theodore Weisman in RLM 12.166
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. Submitted by
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