Quivers from non-orientable surfaces

TL;DR

This paper introduces a method to associate quivers to non-orientable surfaces, enabling the study of their algebraic structures and proving unistructurality for the Mobius strip case.

Contribution

It defines a quiver mutation compatible with quasi-cluster algebras on non-orientable surfaces, extending cluster algebra theory.

Findings

Quivers can be associated to quasi-triangulations of non-orientable surfaces.

Quiver mutation is compatible with quasi-cluster algebra mutation.

The unistructurality of the quasi-cluster algebra from the Mobius strip is established.

Abstract

We associate a quiver to a quasi-triangulation of a non-orientable marked surface and define a notion of quiver mutation that is compatible with quasi-cluster algebra mutation defined by Dupont and Palesi. Moreover, we use our quiver to show the unistructurality of the quasi-cluster algebra arising from the Mobius strip.