Teoría de nudos geométricos e isotopía poligonal

The space of n-sided polygons embedded in euclidean three-space consists of a smoothmanifold in which points correspond to piecewise linear or “geometric” knots, while pathscorrespond to isotopies which preserve the geometric structure of these knots. The topologyof these spaces for the case n = 6 a...

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Main Author: Calvo Soto, Jorge Alberto
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/204
http://hdl.handle.net/10669/12844
id RepoKERWA12844
recordtype dspace
spelling RepoKERWA128442017-08-08T18:50:18Z Teoría de nudos geométricos e isotopía poligonal Teoría de nudos geométricos e isotopía poligonal Calvo Soto, Jorge Alberto The space of n-sided polygons embedded in euclidean three-space consists of a smoothmanifold in which points correspond to piecewise linear or “geometric” knots, while pathscorrespond to isotopies which preserve the geometric structure of these knots. The topologyof these spaces for the case n = 6 and n = 7 is described. In both of these cases, each knotspace consists of five components, but contains only three (when n = 6) or four (when n = 7)topological knot types. Therefore “geometric knot equivalence” is strictly stronger thantopological equivalence. This point is demonstrated by the hexagonal trefoils and heptagonalfigure-eight knots, which, unlike their topological counterparts, are not reversible. Extendingthese results to the cases n 8 will also be discussed.Keywords:  polygonal knots, space polygons, knot spaces, knot invariants. El espacio de los pol´?gonos de n lados, inmersos en el espacio eucl´?deo de tres dimensiones,consiste de una variedad suave en la cual los puntos corresponden a nudos lineales a trozoso “geom´etricos”, mientras que los arcos corresponden a isotop´?as que preservan la estructurageom´etrica de esos nudos. Se describe la topolog´?a de estos espacios para los casos n = 6y n = 7. En ambos casos, cada espacio consta de cinco componentes, aunque contiene s´olotres (cuando n = 6) o cuatro (cuando n = 7) tipos topol´ogicos de nudos. Por lo tanto la“equivalencia geom´etrica de nudos” es estrictamente m´as fuerte que la equivalencia topol´ogica.Este hecho se demuestra con el nudo tr´ebol hexagonal y el nudo doble heptagonal, los cuales,a diferencia de sus contrapartes topol´ogicas, no son reversibles. Se discutir´an tambi´en lasextensiones de estos resultados a los casos n 8.Palabras clave:  nudos poligonales, pol´?gonos espaciales, espacios de nudos, invariantesde nudos. 2015-05-19T18:26:36Z 2015-05-19T18:26:36Z 2009-02-19 00:00:00 2015-05-19T18:26:36Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://revistas.ucr.ac.cr/index.php/matematica/article/view/204 http://hdl.handle.net/10669/12844 10.15517/rmta.v8i2.204 es Revista de Matemática: Teoría y Aplicaciones Vol. 8 Núm. 2 2009 101-130 application/pdf
institution Universidad de Costa Rica
collection Repositorio KERWA
language Español
description The space of n-sided polygons embedded in euclidean three-space consists of a smoothmanifold in which points correspond to piecewise linear or “geometric” knots, while pathscorrespond to isotopies which preserve the geometric structure of these knots. The topologyof these spaces for the case n = 6 and n = 7 is described. In both of these cases, each knotspace consists of five components, but contains only three (when n = 6) or four (when n = 7)topological knot types. Therefore “geometric knot equivalence” is strictly stronger thantopological equivalence. This point is demonstrated by the hexagonal trefoils and heptagonalfigure-eight knots, which, unlike their topological counterparts, are not reversible. Extendingthese results to the cases n 8 will also be discussed.Keywords:  polygonal knots, space polygons, knot spaces, knot invariants.
format Artículo
author Calvo Soto, Jorge Alberto
spellingShingle Calvo Soto, Jorge Alberto
Teoría de nudos geométricos e isotopía poligonal
author_sort Calvo Soto, Jorge Alberto
title Teoría de nudos geométricos e isotopía poligonal
title_short Teoría de nudos geométricos e isotopía poligonal
title_full Teoría de nudos geométricos e isotopía poligonal
title_fullStr Teoría de nudos geométricos e isotopía poligonal
title_full_unstemmed Teoría de nudos geométricos e isotopía poligonal
title_sort teoría de nudos geométricos e isotopía poligonal
publishDate 2015
url http://revistas.ucr.ac.cr/index.php/matematica/article/view/204
http://hdl.handle.net/10669/12844
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