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# Luca Di Cerbo : Extended Graph Manifolds, Dehn Fillings, and Einstein Metrics

In this talk, I will present some new topological obstructions for solving the Einstein equations (in Riemannian signature) on a large class of closed four-manifolds. Finally, I will show that complex-hyperbolic Einstein Dehn filling compactification cannot possibly performed in dimension four. This is in striking contrast with the real-hyperbolic case, and it answers (negatively) a fifteen years old question of Michael Anderson. If time permits, I will conclude with some tantalizing open problems both in dimension four and in higher dimensions. Part of this work is joint with M. Golla (Universit\’e de Nantes).

**Category**: Geometry and Topology**Duration**: 01:14:42**Date**: April 18, 2022 at 3:10 PM-
**Tags:**seminar, Geometry and Topology Seminar

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