A functor-valued invariant of tangles

Khovanov, Mikhail¹

¹Department of Mathematics, University of California, Davis, CA 95616, USA

Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 665-741

Résumé

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.

Détail

DOI : 10.2140/agt.2002.2.665

Keywords: tangles, Jones polynomial, Kauffman bracket, TQFT, complexes, bimodules

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