On maximal fibred submanifolds of a knot exterior
type: Item
instance of: scholarly article
title: On maximal fibred submanifolds of a knot exterior
zbMATH Open document ID: 0651.57007
DOI: 10.1007/BF01442501
author: Osamu Kakimizu
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164569
review text: Let K be a knot in the 3-sphere \(S^ 3\), E its exterior and \(G=\pi_ 1(E)\) the group of K. For an incompressible spanning surface \(S\subset E\) for K, we define a subgroup \(\mu\) (S) of G by \(\mu (S)=\cap_{k\in {\mathbb{Z}}}m^ k\pi_ 1(S)m^{-k}\) where m is the element of G corresponding to a meridian. We prove that \(\mu\) (S) is an invariant for K and it is realized by a compact surface m(S) on S; in particular \(\mu\) (S) is a finitely generated free group. Furthermore it is shown that there is a fibred submanifold F(S) of W with fibre m(S) which is maximal in a sense, and that the pair (F(S),m(S)) is unique up to ambient isotopy of E.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 4062158
zbMATH Keywords: knot in the 3-sphere
zbMATH Keywords: incompressible spanning surface
zbMATH Keywords: fibred submanifold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4062158