A categorification of the Jones polynomial
Mikhail Khovanov
TL;DR
This paper introduces a new bigraded cohomology theory for links that categorifies the Jones polynomial, providing a richer algebraic invariant.
Contribution
It presents the first categorification of the Jones polynomial through a bigraded cohomology theory, expanding the algebraic tools for knot invariants.
Findings
Defines a bigraded cohomology theory for links
Shows the Euler characteristic matches the Jones polynomial
Provides new algebraic invariants for knot theory
Abstract
We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics