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Sharpness of proper cocompact actions and applications

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Fanny Kassel
Elia Fioravanti, Ursula Hamenstädt, Stephan Stadler
Don, 05/05/2022 - 10:30 - 11:30

This talk will take place in the lecture hall in person only.
Not available via zoom.

We prove the so-called Sharpness Conjecture: any properly discontinuous and cocompact action of a discrete group on a real reductive homogeneous space G/H satisfies a strong form of properness called sharpness. This has applications e.g. to the deformation of proper cocompact actions, through a link to Anosov representations. It also allows us to deduce the nonexistence of proper cocompact actions on certain homogeneous spaces such as SL(2n,R)/SL(2n-k,R) for k=1 or 2. Joint work with Nicolas Tholozan. 

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