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Knot homology via derived categories of coherent sheaves. IV: Coloured links. (English) Zbl 1378.14011

Summary: 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.
For Part I and II, see [the authors, Duke Math. J. 142, No. 3, 511–588 (2008; Zbl 1145.14016); Invent. Math. 174, No. 1, 165–232 (2008; Zbl 1298.57007)].

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
18F30 Grothendieck groups (category-theoretic aspects)
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
18E30 Derived categories, triangulated categories (MSC2010)
14M15 Grassmannians, Schubert varieties, flag manifolds
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