Algebraic and Geometric Topology 2 (2002),
paper no. 30, pages 665-741.
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.
Tangles, Jones polynomial, Kauffman bracket, TQFT, complexes, bimodules
AMS subject classification.
Secondary: 57M27, 16D20, 18G60.
Submitted: 21 February 2002.
Accepted: 25 April 2002.
Published: 6 September 2002.
Notes on file formats
Department of Mathematics, University of California
Davis, CA 95616, USA
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