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Abstract
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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.
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Keywords
tangles, Jones polynomial, Kauffman bracket, TQFT,
complexes, bimodules
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 16D20, 18G60
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Publication
Received: 21 February 2002
Accepted: 25 April 2002
Published: 6 September 2002
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