Braid groups and Kleinian singularities
Christopher Brav, Hugh Thomas
TL;DR
This paper proves that certain braid group actions related to ADE configurations are faithful, using Garside structures, which helps in understanding stability conditions for Kleinian singularities.
Contribution
It establishes the faithfulness of braid group actions generated by twists along ADE configurations in derived categories, utilizing Garside structures.
Findings
Faithfulness of braid group actions proven
Garside structure applied to ADE braid groups
Supports Bridgeland's stability conditions for Kleinian singularities
Abstract
We establish faithfulness of braid group actions generated by twists along an ADE configuration of -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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic structures and combinatorial models