Coxeter groups, quiver mutations and geometric manifolds

Felikson, A.; Tumarkin, P.

Abstract

We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh, and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every quiver or diagram of finite or affine type a CW-complex with a proper action of a finite (or affine) Coxeter group. These CW-complexes undergo mutations agreeing with mutations of quivers and diagrams. We also generalize the construction to quivers and diagrams originating from unpunctured surfaces and orbifolds.

Citation

Felikson, A., & Tumarkin, P. (2016). Coxeter groups, quiver mutations and geometric manifolds. Journal of the London Mathematical Society, 94(1), 38-60. https://doi.org/10.1112/jlms/jdw023

• Journal Article Type: Article
• Acceptance Date: Apr 4, 2016
• Online Publication Date: May 24, 2016
• Publication Date: Aug 1, 2016
• Deposit Date: Sep 4, 2015
• Publicly Available Date: Apr 5, 2016
• Journal: Journal of the London Mathematical Society
• Print ISSN: 0024-6107
• Electronic ISSN: 1469-7750
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 94
• Issue: 1
• Pages: 38-60
• DOI: https://doi.org/10.1112/jlms/jdw023
• Related Public URLs: http://arxiv.org/abs/1409.3427