Uniqueness of minimal genus Seifert surfaces for links
type: Item
instance of: scholarly article
title: Uniqueness of minimal genus Seifert surfaces for links
zbMATH Open document ID: 0684.57001
DOI: 10.1016/0166-8641(89)90107-7
author: Tsuyoshi Kobayashi
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The author studies the problem suggested by the title. Let \(L_ 1\), \(L_ 2\) be links with minimal genus Seifert surfaces \(R_ 1\), \(R_ 2\). Let R be a Murasugi sum of \(R_ 1\) and \(R_ 2\). The author proves the following: The minimal genus Seifert surfaces for \(L=\partial R\) are unique if and only if one of the \(L_ i\) is fibered, and the minimal genus Seifert surfaces for the other are unique. Knots with non-unique, minimal genus Seifert surfaces with fewer than 11 crossing are listed.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4121030
zbMATH Keywords: fibred knots
zbMATH Keywords: links
zbMATH Keywords: minimal genus Seifert surfaces
zbMATH Keywords: Murasugi sum
reviewed by: Lee P. Neuwirth
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90107-7
OpenAlex ID: W2029779332
cites work: Complements of minimal spanning surfaces of knots are not unique
cites work: Knots with Infinitely Many Minimal Spanning Surfaces
cites work: The Murasugi sum is a natural geometric operation
cites work: Foliations and the topology of 3-manifolds
cites work: Foliations and genera of links
cites work: Detecting fibred links in \(S^ 3\)
cites work: Q3709484
cites work: Incompressible surfaces in 2-bridge knot complements
cites work: Free Surfaces in S 3
cites work: On Simple Loops on a Solid Torus of General Genus
cites work: Q4207380
cites work: Simple Knots Without Unique Minimal Surfaces
cites work: Q4107635
cites work: Sutured manifolds and generalized Thurston norms
cites work: Finding Disjoint Seifert Surfaces
cites work: Q3709485
cites work: On irreducible 3-manifolds which are sufficiently large
cites work: Isotopy types of knot spanning surfaces
description: scientific article; zbMATH DE number 4121030