Coxeter groups, quiver mutations and geometric manifolds
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.
Keywords
Cite
@article{arxiv.1409.3427,
title = {Coxeter groups, quiver mutations and geometric manifolds},
author = {Anna Felikson and Pavel Tumarkin},
journal= {arXiv preprint arXiv:1409.3427},
year = {2019}
}
Comments
22 pages, lots of figures; v2: minor changes (including Remarks 5.6 and 5.7), references updated. To appear in J. London Math. Soc