Homology, Homotopy and Applications

Volume 9 (2007)

Number 2

Braid cobordisms, triangulated categories, and flag varieties

Pages: 19 – 94

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n2.a2


Mikhail Khovanov (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Richard Thomas (Department of Mathematics, Imperial College, London, United Kingdom)


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 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.


derived categories, triangulated categories, braid group actions, braid cobordisms, categorification, flag varieties, Fukaya categories, mirror symmetry

2010 Mathematics Subject Classification


Published 1 January 2007