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Coxeter groups, quiver mutations and geometric manifolds.

Felikson, A. and Tumarkin, P. (2016) 'Coxeter groups, quiver mutations and geometric manifolds.', Journal of the London Mathematical Society., 94 (1). pp. 38-60.


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.

Item Type:Article
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Publisher 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:
Date accepted:04 April 2016
Date deposited:05 April 2016
Date of first online publication:24 May 2016
Date first made open access:No date available

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