Braid groups and Kleinian singularities

2009/10/14 by Brav, Christopher, Thomas, Hugh · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0910.2521

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.

Cited by

• Quiver braid group action for a 3-fold crepant resolution
• Extriangulated structures from stability conditions and application to braid representations
• Spherical and Semibrick Classifications
• Configurations of Lagrangian spheres in K3 surfaces
• Faithful Burau-like representations of some rank two Garside groups and torus knot groups

Related

• Faithful actions of braid groups by twists along ADE-configurations of spherical objects
• Braid group actions on derived categories of coherent sheaves
• Mirror symmetry and actions of braid groups on derived categories
• Garside elements, inertia and Galois action on braid groups
• The 3-strand braid group with torsion