Kaiser, Uwe 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]. Reviewer: Anna Beliakova (Basel) Cited in 1 ReviewCited in 2 Documents 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 Keywords:3-manifold; incompressible surface; Frobenius algebra; skein module; Bar-Natan relation PDFBibTeX XMLCite \textit{U. Kaiser}, Banach Cent. Publ. 85, 59--81 (2009; Zbl 1181.57008) Full Text: DOI arXiv