# Frobenius algebras and skein modules of surfaces in 3-manifolds

Banach Center Publications (2009)

- Volume: 85, Issue: 1, page 59-81
- ISSN: 0137-6934

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topUwe Kaiser. "Frobenius algebras and skein modules of surfaces in 3-manifolds." Banach Center Publications 85.1 (2009): 59-81. <http://eudml.org/doc/282154>.

@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 -

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