INSTITUTE OF MATHEMATICS · POLISH ACADEMY OF SCIENCES
BANACH CENTER
PUBLICATIONS
ISSN: 0137-6934(p) 1730-6299(e)
Frobenius algebras and skein modules of surfaces in 3-manifolds
Uwe Kaiser1 Banach Center Publ. 85 (2009), 59-81
doi:10.4064/bc85-0-4 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.
