Algebraic and Geometric Topology 2 (2002), paper no. 30, pages 665-741.

A functor-valued invariant of tangles

Mikhail Khovanov

Abstract. We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this invariant descends to the Kauffman bracket of the tangle. When the tangle is a link, the invariant specializes to the bigraded cohomology theory introduced in our earlier work.

Keywords. Tangles, Jones polynomial, Kauffman bracket, TQFT, complexes, bimodules

AMS subject classification. Primary: 57M25. Secondary: 57M27, 16D20, 18G60.

DOI: 10.2140/agt.2002.2.665

E-print: arXiv:math.QA/0103190

Submitted: 21 February 2002. Accepted: 25 April 2002. Published: 6 September 2002.

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Mikhail Khovanov
Department of Mathematics, University of California
Davis, CA 95616, USA
Email: mikhail@math.ucdavis.edu

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