Braid groups and Kleinian singularities

Understand

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.