Categorification of the Jones–Wenzl projectors

  • Benjamin Cooper

    University of Virginia, Charlottesville, USA
  • Vyacheslav Krushkal



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 the are 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 and a categorification of quantum spin networks. We introduce 6j-symbols in this context.

Cite this article

Benjamin Cooper, Vyacheslav Krushkal, Categorification of the Jones–Wenzl projectors. Quantum Topol. 3 (2012), no. 2, pp. 139–180

DOI 10.4171/QT/27