Work

Punctured Surfaces, Quiver Mutations, and Quotients of Coxeter Groups

Year: 2025

Type: article

Abstract: In [1], Barot and Marsh provided an explicit construction of presentation of a finite Weyl group $W$ by any quiver mutation-equivalent to an orientation of a Dynkin diagram with Weyl group $W$. The construction was extended in [8] to obtain presentations for all affine Coxeter groups, as well as to construct groups from triangulations of unpunctured surfaces and orbifolds, where the groups are invariant under change of triangulation and thus are presented as quotients of numerous distinct Coxeter groups. We extend the construction to include most punctured surfaces and orbifolds, providing a new invariant for almost all marked surfaces.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf320

Authors: Anna Felikson, Michael Shapiro, Pavel Tumarkin

Institutions: Durham University, Michigan State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

Funders: National Science Foundation, Leverhulme Trust