Cautis, Sabin; Kamnitzer, Joel Knot homology via derived categories of coherent sheaves. IV: Coloured links. (English) Zbl 1378.14011 Quantum Topol. 8, No. 2, 381-411 (2017). 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)]. Cited in 6 Documents 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 Keywords:coherent sheaves; derived categories; knot homologies; Khovanov homology; deformed homologies; spectral sequences; affine Grassmannian; convolution varieties Citations:Zbl 1145.14016; Zbl 1298.57007 PDFBibTeX XMLCite \textit{S. Cautis} and \textit{J. Kamnitzer}, Quantum Topol. 8, No. 2, 381--411 (2017; Zbl 1378.14011) Full Text: DOI arXiv