Spaces of Bridgeland stability conditions in representation theory

TL;DR

This paper introduces the space of Bridgeland stability conditions in the context of representation theory, highlighting its structure and examples, including the Bridgeland-Smith correspondence for quiver categories from marked surfaces.

Contribution

It provides an accessible introduction to Bridgeland stability conditions with a focus on representation theory examples and the Bridgeland-Smith correspondence.

Findings

Description of the complex manifold structure of stability conditions

Examples from representation theory, especially quiver categories

Review of Bridgeland-Smith correspondence for marked surfaces

Abstract

The space of Bridgeland stability conditions is a complex manifold that can be attached to a triangulated category, of which it encodes some homological properties. These notes are an introduction to this topic, with a focus on examples from representation theory, and review the example of the Bridgeland-Smith correspondence for some quiver categories from marked surfaces.