Visualization of A'Campo's fibered links and unknotting operation
type: Item
instance of: scholarly article
title: Visualization of A'Campo's fibered links and unknotting operation
zbMATH Open document ID: 1016.57006
DOI: 10.1016/S0166-8641(01)00124-9
author: Mikami Hirasawa
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: The author gives an algorithmic method to draw the link of a ``divide''. Recall that divides were defined by N. A'Campo and are generic relative immersions in the unit disk of a finite number of 1-manifolds (i.e. intervals and circles). Following A'Campo one can associate a fibered link to a divide. The method presented by the author is applied to slalom divides to prove that the link associated to a slalom divide is arborescent. Moreover, the author gives an algorithmic construction of a Seifert surface associated to a link coming from a divide. Using these Seifert surfaces he can compute the unknotting number of a link associated to a one branch divide.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1787530
zbMATH Keywords: divide
zbMATH Keywords: link
zbMATH Keywords: slalom divide
zbMATH Keywords: slalom knot
zbMATH Keywords: unknotting operation
zbMATH Keywords: Seifert surface
zbMATH Keywords: unknotting number
MaRDI profile type: Publication
cites work: Real deformations and complex topology of plane curve singularities
cites work: Generic immersions of curves, knots, monodromy and Gordian number
cites work: Planar trees, slalom curves and hyperbolic knots
cites work: Q3687355
cites work: Q5601331
cites work: Detecting fibred links in \(S^ 3\)
cites work: Links of oriented divides and fibrations in link exteriors
cites work: Half plane models for divides, their knots and Dowker-Thistlethwaite codes
cites work: Q4845496
cites work: Four-genus and unknotting number of positive knots and links
cites work: The link of an extrovert divide
cites work: Q4107635
cites work: Quasipositivity as an obstruction to sliceness
cites work: Q4486731
cites work: Minimal genus Seifert surfaces for special arborescent links
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description: scientific article; zbMATH DE number 1787530