A functor-valued invariant of tangles

Details A functor-valued invariant of tangles A functor-valued invariant of tangles

2001-03-27

arxiv.org/abs/math/0103190v2

Algebr. Geom. Topol. 2 (2002) 665-741

Mathematics

Quantum Algebra

77 pages, 46 eps figures. Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-30

Scientific paper

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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