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Matrix factorizations and link homology
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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.
Forward citations
Cited by 4 Pith papers
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HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
Links in genus-g handlebodies are assigned a triply-graded homology built from singular Soergel bimodules and Hochschild cohomology, generalizing colored HOMFLYPT homology.
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Bipartite expansion beyond biparticity
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...
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$q$-Series Invariants of Three-Manifolds and Knots-Quivers Correspondence
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.
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A survey of knots and quivers
This is a review of knot polynomials, triply-graded knot homologies, and the knots-quivers correspondence, with no new results.
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