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Topics in Geometric Group Theory |
| November 05, 2007 to November 09, 2007 |
| Organized By: Noel Brady, Mike Davis, Mark Feighn |
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| Parent Programs: |
| Geometric Group Theory |
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| Return to Workshop Description |
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A family of simple groups acting on buildings
Wednesday November 7, 2007
09:00AM - 09:50AM
Speakers:
Bertrand REMY
Abstract:
[Joint work with Pierre-Emmanuel Caprace]
Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned building. Using some weak hyperbolic properties of non virtually abelian Coxeter groups, we prove that these lattices are simple if the corresponding buildings are (irreducible and) not of affine type (i.e. they are not Bruhat-Tits buildings). In fact, many
of them are finitely presented and enjoy property (T). Our arguments explain geometrically why simplicity fails to hold only for affine Kac-Moody groups (i.e. arithmetic groups). If time permits, we will also explain how we prove that a nontrivial continuous homomorphism from a completed Kac-Moody group is always proper, and that Kac-Moody lattices fulfill conditions implying strong superrigidity properties for isometric actions on non-positively curved metric spaces.
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