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An Experimental Study of Seifert Fibered Dehn Surgery via SnapPea

An experimental study of Seifert fibered Dehn surgery via SnapPea
Authors: Kimihiko Motegi;

An Experimental Study of Seifert Fibered Dehn Surgery via SnapPea

Abstract

In [Commun. Anal. Geom. 7, 551--583 (1999; Zbl 0940.57025)], \textit{K. Miyazaki} and \textit{K. Motegi} studied Seifert fibered surgeries on hyperbolic knots from the viewpoint of ``locating Seifert fibers'', and made use of Jeff Week's computer program SnapPea (freely available from http://humber.northnet.org/weeks/SnapPea.html) in order to investigate a relationship between closed geodesics in hyperbolic knot complements and Seifert fibers after Seifert fibered surgeries on them. In the present paper, the author explains how they obtained their experimental results with SnapPea. He demonstrates how SnapPea may be used in order to perform a lot of experiments concerning knot complements and surgery (for example: how to check whether a given knot is hyperbolic or whether a Dehn surgered manifold is hyperbolic, or how to find curves in knot complements which become fibers after Seifert fibered surgery\dots). The paper also contains some proposed questions, inspired by the computer experiments.

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Keywords

Topology of general \(3\)-manifolds, computer program SnapPea, Seifert fibered space, hyperbolic knot, Knots and links in the \(3\)-sphere, Software, source code, etc. for problems pertaining to manifolds and cell complexes, Surgery and handlebodies, Dehn surgery

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
gold