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> Twists and braids for general threefold flops If a complex surface contains a (-2)-curve, this curve corresponds to a spherical object in the derived category of coherent sheaves on the surface. For certain arrangements of such curves,

> Twists and braids for general threefold flops If a complex surface contains a (-2)-curve, this curve corresponds to a spherical object in the derived category of coherent sheaves on the surface. For certain arrangements of such curves, Seidel and Thomas used these objects to establish a braid group action on the derived category. I explain joint work with Michael Wemyss giving a generalisation to curves on threefolds: this uses braid-type groups associated to hyperplane arrangements, and relative spherical objects over noncommutative base rings.

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