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.

1. Department of Mathematics
   Boise State University
   1910 University Drive
   Boise, ID 83725-1555, U.S.A.