📁Homological algebra, triangulated and abelian categories, algebraic combinatorics

Gentle algebras and oriented surfaces with boundary

Supervisor: Rosanna Laking

Description

The gentle algebras are a family of finite-dimensional algebras characterised by their associated bound quivers having particularly nice combinatorial properties. Recent work of Opper-Plamondon-Schroll and Baur-Coelho Simões shows that every gentle algebra is determined by an oriented surface with boundary, and the associated category of modules and its derived category can be encoded by homotopy classes of curves on the surface.