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In analogy to how 3d TQFTs are induced from quantum groups/Hopf algebras/ and generally bialgebras (hence 3-modules, the higher space of quantum states assigned to the point which by the cobordism theorem defines the theory) one may build 4d TQFTs from higher analogs of these, namely models of 4-modules given by algebraic structures such as trialgebras and Hopf categories.
Walker-Zhang model?
4d TQFT
Original references include
Louis Crane, Louis Kauffman, David Yetter, State-Sum invariants of 4-manifolds I (pdf)
Louis Crane, Igor Frenkel, Four dimensional topological quantum field theory, Hopf categories, and the canonical bases, J.Math.Phys. 35 (1994) 5136-5154, (arXiv:hep-th/9405183)
See also
Construction via factorization homology from braided tensor categories (with relation to double affine Hecke algebras) is discussed in
Many more should eventually go here…
Last revised on October 15, 2015 at 10:36:14. See the history of this page for a list of all contributions to it.