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The flat closing problem

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  • UserBruno Martelli (Università di Pisa)
  • ClockFriday 06 February 2026, 13:45-14:45
  • HouseMR13.

If you have a question about this talk, please contact Macarena Arenas .

The Flat Closing Problem is the following 1993 question of Gromov: Let X be a proper CAT space and Γ be a discrete group acting properly and co-compactly by isometries on X. Does the existence of a flat plane in X imply that Γ contains a copy of ZxZ? We will show that this question has a negative answer. The counterexample arises from a 4-dimensional pseudo-Anosov homeomorphism whose mapping torus is a hyperbolic 5-manifold.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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