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A categorification of the Jones polynomial. (English) Zbl 0960.57005

The author associates to each diagram \(D\) of a link \(L\) in three-space a chain complex \(C(D)\) of graded \(Z[c]\)-modules, where \(c\) is an indeterminate of degree 2. The graded cohomology of \(C(D)\) is a link type invariant of \(L\) whose graded Euler characteristic determines the Kauffman bracket, and hence the Jones polynomial, of \(L\).

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
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References:

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