The braid group for a quiver with superpotential

TL;DR

This paper surveys different generalizations of braid groups associated with quivers with superpotentials, emphasizing cluster braid groups and their relevance to cluster algebras, Calabi-Yau categories, and stability conditions.

Contribution

It compares various braid group generalizations and highlights the role of cluster braid groups in the context of quivers with superpotentials.

Findings

Cluster braid groups are introduced and compared.

Connections to cluster algebras and Calabi-Yau categories are discussed.

The work relates braid groups to Bridgeland stability conditions.

Abstract

We survey and compare various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with A.~King. Our motivations come from the study of cluster algebras, Calabi-Yau categories and Bridgeland stability conditions.