Categorification of the Jones-Wenzl Projectors

Details Categorification of the Jones-Wenzl Projectors Categorification of the Jones-Wenzl Projectors

2010-05-27

arxiv.org/abs/1005.5117v3

Quantum Topol. 3 (2012), 139-180

Mathematics

Geometric Topology

44 pages

Scientific paper

The Jones-Wenzl projectors play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes whose graded Euler characteristic is the "classical" projector in the Temperley-Lieb algebra. We show that they are homotopy idempotents and uniquely defined up to homotopy. Our results fit within the general framework of Khovanov's categorification of the Jones polynomial. Consequences of our construction include families of knot invariants corresponding to higher representations of quantum su(2) and a categorification of quantum spin networks. We introduce 6j-symbols in this context.

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