Braid cobordisms, triangulated categories, and flag varieties
arXiv:math/0609335
Abstract
We argue that various braid group actions on triangulated categories should be extended to projective actions of the category of braid cobordisms and illustrate how this works in examples. We also construct actions of both the affine braid group and the braid cobordism category on the derived category of coherent sheaves on the cotangent bundle to the full flag variety.
arXiv commentComment added noting faithfulness of braid group action on D(T*Flag). Referee's comments incorporated to make paper more readable. 90 pages, 21 figures
References in corpus (6)
- Khovanov's homology for tangles and cobordisms
- Semiorthogonal decomposition for algebraic varieties
- A functor-valued invariant of tangles
- The Mukai pairing, I: the Hochschild structure
- TQFT with corners and tilting functors in the Kac-Moody case
- Triply-graded link homology and Hochschild homology of Soergel bimodules