Braid groups and Kleinian singularities

Abstract

We establish faithfulness of braid group actions generated by twists along an ADE configuration of $2$-spherical objects in a derived category. Our major tool is the Garside structure on braid groups of type ADE. This faithfulness result provides the missing ingredient in Bridgeland's description of a space of stability conditions associated to a Kleinian singularity.

Section 4 from versions 1 and 2 has been deleted due to an error in the proof of Theorem 2. Renamed the paper and rewrote the other sections to reflect this change