A functor-valued invariant of tangles

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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27, 16D20, 18G60

References

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Publication

Received: 21 February 2002

Accepted: 25 April 2002

Published: 6 September 2002

Authors

Mikhail Khovanov
Department of Mathematics University of California Davis, CA 95616 USA

Volume 2, issue 2 (2002)

Mikhail Khovanov