2010-02-19

Chris Brav (University of Toronto)

Braid groups and Kleinian singularities, II

We review how the spherical twists of Seidel and Thomas can be used to construct a braid group action of type A,D, or E on the derived category of coherent sheaves on the minimal resolution of a Kleinian singularity. By work of Khovanov, Seidel, and Thomas, this action was known to be faithful in type A. We extend this faithfulness result to all types and then construct an action of an extended affine braid group, which we conjecture to be faithful. Our faithfulness result provides the missing ingredient for completing Bridgeland's description of spaces of stability conditions for certain triangulated categories associated to Kleinian singularities. This is joint work with Hugh Thomas from the University of New Brunswick.