Frobenius Algebras and Skein Modules of Surfaces in 3-Manifolds
For each (commutative) Frobenius algebra there is defined a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural extension of the corresponding topological quantum field theory. In particular the skein module of the 3-ball is isomorphic to the ground ring of the Frobenius algebra. We prove a presentation theorem for the skein module with generators incompressible surfaces colored by elements of a generating set of the Frobenius algebra, and with relations determined by tubing geometry in the manifold and relations of the algebra.
Kaiser, Uwe. (2009). "Frobenius Algebras and Skein Modules of Surfaces in 3-Manifolds". Banach Center Publications, 8559-81. https://doi.org/10.4064/bc85-0-4