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.
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Brav, C., Thomas, H. Braid groups and Kleinian singularities. Math. Ann. 351, 1005–1017 (2011). https://doi.org/10.1007/s00208-010-0627-y
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DOI: https://doi.org/10.1007/s00208-010-0627-y