Teor?a de nudos geom?tricos e isotop?a 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
Summary: 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.