#### Title

Frobenius Algebras and Skein Modules of Surfaces in 3-Manifolds

#### Document Type

Article

#### Publication Date

1-1-2009

#### Abstract

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.

#### Publication Information

Kaiser, Uwe. (2009). "Frobenius Algebras and Skein Modules of Surfaces in 3-Manifolds". *Banach Center Publications,** 85*59-81. http://dx.doi.org/10.4064/bc85-0-4