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...

Descripción completa

Autor Principal: Calvo Soto, Jorge Alberto
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/204
http://hdl.handle.net/10669/12844
Sumario: 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.