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A categorification of the Jones polynomial

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arxiv math/9908171 v2 pith:BJCK3BOW submitted 1999-08-30 math.QA

Mikhail Khovanov This is my paper · ORCID
classification math.QA
keywords jonespolynomialbigradedcategorificationcharacteristiccohomologyconstructeuler
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We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.

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Cited by 9 Pith papers

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

  1. A supergroup series for knot complements

    math.GT 2025-08 unverdicted novelty 7.0 of 10

    Defines the three-variable superalgebra series F_K(y,z,q) for knot complements, derives its surgery relation to hat Z(q), and computes examples for torus knots.

  2. 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.

  3. 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...

  4. Path to homology of Yang-Baxter operators

    math.GT 2026-07 accept novelty 5.5 of 10

    A historical and personal survey of the path from knot theory and distributive homology to Yang-Baxter homology, including new homology computations for HOMFLYPT operators and a cubic face-map decomposition of the Rei...

  5. Categorification of some Penrose polynomials

    math.CO 2026-07 unverdicted novelty 5.0 of 10

    Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.

  6. More on Kashaev limits of the quantum $A$-polynomials

    hep-th 2026-06 unverdicted novelty 3.0 of 10

    In the Kashaev limit the non-homogeneous quantum A-polynomial splits into phases tied to zero action and deformed hyperbolic volume, with a byproduct expectation that the classical A-polynomial at L=1 is proportional ...

  7. Khovanov complexes for bipartite links

    hep-th 2026-05 unverdicted novelty 2.0 of 10

    Shows that the Kauffman-Khovanov 2²-hypercube reduces to the bipartite 3-hypercube for N=2, confirming consistency of the reduction for bipartite links.

  8. Quantum invariants of 3-manifolds and links: a review

    math-ph 2025-09 unverdicted novelty 1.0 of 10

    This is a survey, not a new result: it reviews the q-series invariants Zhat, F_K, F_L and their supergroup analogues, collecting known conjectures, theorems, and examples.

  9. 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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