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A functor-valued invariant of tangles. (English) Zbl 1002.57006

Summary: 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 [Duke Math. J. 101, No. 3, 359-426 (1999; Zbl 0960.57005)].

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
16D20 Bimodules in associative algebras
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
18G60 Other (co)homology theories (MSC2010)

Citations:

Zbl 0960.57005
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