Proper affine actions of rightangled Coxeter groups
Introductory Workshop: Geometric Group Theory August 22, 2016  August 26, 2016
Location: SLMath:
geometric group theory
hyperbolic group
Auslander conjecture
affine buildings and cells
affine geometry
Lie groups
quadratic forms
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
20C05  Group rings of finite groups and their modules (grouptheoretic aspects) [See also 16S34]
14600
The Auslander Conjecture states that all discrete groups acting properly and cocompactly on R^n by affine transformations should be virtually solvable. In 1983, Margulis constructed the first examples of proper (but not cocompact) affine actions of nonabelian free groups. It seems that until now all known examples of irreducible proper affine actions were by virtually solvable or virtually free groups. I will explain that any rightangled Coxeter group on k generators admits a proper affine action on R^{k(k1)/2}. This is joint work with J. Danciger and F. Guéritaud.
Kassel Notes

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