Frobenius algebras and skein modules of surfaces in 3-manifolds

@article{UweKaiser2009,
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.},
author = {Uwe Kaiser},
journal = {Banach Center Publications},
keywords = {3-manifold; incompressible surface; Frobenius algebra; skein module; Bar-Natan relation},
language = {eng},
number = {1},
pages = {59-81},
title = {Frobenius algebras and skein modules of surfaces in 3-manifolds},
url = {http://eudml.org/doc/282154},
volume = {85},
year = {2009},
}

TY - JOUR
AU - Uwe Kaiser
TI - Frobenius algebras and skein modules of surfaces in 3-manifolds
JO - Banach Center Publications
PY - 2009
VL - 85
IS - 1
SP - 59
EP - 81
AB - 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.
LA - eng
KW - 3-manifold; incompressible surface; Frobenius algebra; skein module; Bar-Natan relation
UR - http://eudml.org/doc/282154
ER -