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1 September 2020 Proper affine actions for right-angled Coxeter groups
Jeffrey Danciger, François Guéritaud, Fanny Kassel
Duke Math. J. 169(12): 2231-2280 (1 September 2020). DOI: 10.1215/00127094-2019-0084

Abstract

For any right-angled Coxeter group Γ on k generators, we construct proper actions of Γ on O ( p , q + 1 ) by right-and-left multiplication and on the Lie algebra o ( p , q + 1 ) by affine transformations, for some p , q N with p + q + 1 = k . As a consequence, any virtually special group admits proper affine actions on some R n : this includes in particular surface groups, hyperbolic 3 -manifold groups, and examples of word hyperbolic groups of arbitrarily large virtual cohomological dimension. We also study some examples in cohomological dimensions two and four, for which the dimension of the affine space may be substantially reduced.

Citation

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Jeffrey Danciger. François Guéritaud. Fanny Kassel. "Proper affine actions for right-angled Coxeter groups." Duke Math. J. 169 (12) 2231 - 2280, 1 September 2020. https://doi.org/10.1215/00127094-2019-0084

Information

Received: 8 June 2018; Revised: 14 October 2019; Published: 1 September 2020
First available in Project Euclid: 11 August 2020

MathSciNet: MR4139042
Digital Object Identifier: 10.1215/00127094-2019-0084

Subjects:
Primary: 20H15
Secondary: 57M50

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 12 • 1 September 2020
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