Homology, Homotopy and Applications

Braid cobordisms, triangulated categories, and flag varieties

Mikhail Khovanov and Richard Thomas

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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 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.

Article information

Source
Homology Homotopy Appl., Volume 9, Number 2 (2007), 19-94.

Dates
First available in Project Euclid: 23 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.hha/1201127331

Mathematical Reviews number (MathSciNet)
MR2366943

Zentralblatt MATH identifier
1119.18008

Subjects
Primary: 18E30: Derived categories, triangulated categories

Keywords
Derived categories triangulated categories braid group actions braid cobordisms categorification flag varieties Fukaya categories mirror symmetry

Citation

Khovanov, Mikhail; Thomas, Richard. Braid cobordisms, triangulated categories, and flag varieties. Homology Homotopy Appl. 9 (2007), no. 2, 19--94. https://projecteuclid.org/euclid.hha/1201127331


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