Quantum Topology


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Volume 8, Issue 2, 2017, pp. 381–411
DOI: 10.4171/QT/93

Published online: 2017-05-29

Knot homology via derived categories of coherent sheaves IV, coloured links

Sabin Cautis[1] and Joel Kamnitzer[2]

(1) University of British Columbia, Vancouver, Canada
(2) University of Toronto, Canada

We define a deformation of our earlier link homologies for fundamental representations of $\mathfrak {sl}_m$. The deformed homology of a link is isomorphic to the deformed homology of the disjoint union of its components. Moreover, there exists a spectral sequence starting with the old homology and converging to this deformed homology.

Keywords: Coherent sheaves, derived categories, knot homologies, Khovanov homology, deformed homologies, spectral sequences, affine Grassmannian, convolution varieties

Cautis Sabin, Kamnitzer Joel: Knot homology via derived categories of coherent sheaves IV, coloured links. Quantum Topol. 8 (2017), 381-411. doi: 10.4171/QT/93