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Frobenius algebras and skein modules of surfaces in 3-manifolds. (English) Zbl 1181.57008

Golasiński, Marek (ed.) et al., Algebraic topology – old and new. M. M. Postnikov memorial conference, Będlewo, Poland, June 18–24, 2007. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-04-1/pbk). Banach Center Publications 85, 59-81 (2009).
For each commutative Frobenius algebra, the author defines a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system on its boundary. The skein relations are local and generalize those founded by Bar-Natan in the context of Khovanov’s homology. It is shown that given a system of curves on the boundary, the corresponding skein module is generated by incompressible surfaces in \(M\) bounding these curves.
For the entire collection see [Zbl 1162.00013].

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)
57R42 Immersions in differential topology
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