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2002 A functor-valued invariant of tangles
Mikhail Khovanov
Algebr. Geom. Topol. 2(2): 665-741 (2002). DOI: 10.2140/agt.2002.2.665

Abstract

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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Mikhail Khovanov. "A functor-valued invariant of tangles." Algebr. Geom. Topol. 2 (2) 665 - 741, 2002. https://doi.org/10.2140/agt.2002.2.665

Information

Received: 21 February 2002; Accepted: 25 April 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1002.57006
MathSciNet: MR1928174
Digital Object Identifier: 10.2140/agt.2002.2.665

Subjects:
Primary: 57M25
Secondary: 16D20, 18G60, 57M27

Rights: Copyright © 2002 Mathematical Sciences Publishers

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