Frobenius algebras and skein modules of surfaces in 3-manifolds

• Autorzy: Uwe Kaiser
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57M35: Dehn's lemma, sphere theorem, loop theorem, asphericity
• 57R42: Immersions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 85
• Numer: 1
• Strony: 59-81

Daty

wydano

2009

Twórcy

autor

Uwe Kaiser

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

Identyfikatory

DOI

10.4064/bc85-0-4