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Matrix factorizations and link homology

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arxiv math/0401268 v2 pith:5SV4LHAL submitted 2004-01-21 math.QA

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keywords polynomialtheoryfactorizationshomologylinksmatrixalgebrabuild
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For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. HOMFLYPT homology for links in handlebodies via type A Soergel bimodules

    math.QA 2019-08 accept novelty 7.0 of 10

    Links in genus-g handlebodies are assigned a triply-graded homology built from singular Soergel bimodules and Hochschild cohomology, generalizing colored HOMFLYPT homology.

  2. Bipartite expansion beyond biparticity

    hep-th 2025-01 conditional novelty 6.0 of 10

    The authors construct positive decompositions of fundamental HOMFLY polynomials in variables φ, φ̄, D for arbitrary knots, not just bipartite ones, and give a criterion to detect when such a decomposition conceals a b...

  3. $q$-Series Invariants of Three-Manifolds and Knots-Quivers Correspondence

    math-ph 2024-12 conditional novelty 4.0 of 10

    Z-hat three-manifold invariants are shown to depend only on the Lie algebra, and a quiver matrix block structure is conjectured for double twist knots.

  4. A survey of knots and quivers

    math.GT 2025-05 unverdicted

    This is a review of knot polynomials, triply-graded knot homologies, and the knots-quivers correspondence, with no new results.

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