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Coxeter groups, quiver mutations and geometric manifolds

Felikson, A.; Tumarkin, P.

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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 Mar 28, 2024
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

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Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in the Journal of the London Mathematical Society following peer review. The version of record is available online at: http://dx.doi.org/10.1112/jlms/jdw023




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