The AG-invariant for (m+2)-angulations

Abstract

In this paper, we study gentle algebras that come from (m+2)-angulations of unpunctured Riemann surfaces with boundary and marked points. We focus on calculating a derived invariant introduced by Avella-Alaminos and Geiss, generalizing previous work done when m=1. In particular, we provide a method for calculating this invariant based on the the configuration of the arcs in the (m+2)-angulation, the marked points, and the boundary components.