Representations of (1,1)-knots

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We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus. The second representation is parametric: every (1,1)-knot can be represented by a 4-tuple of integer parameters. The strict connection of this representation with the class of Dunwoody manifolds is illustrated. The above representations are explicitly obtained in some interesting cases, including two-bridge knots and torus knots.
16 pages, 7 figures. To appear in Fundamenta Mathematicae, special volume Proceedings of Knots in Poland, vol. II

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Geometric Topology, 57M25; 57M12

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http://salesiana.dossiersoluciones.com/handle/123456789/101022

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501234
 http://arxiv.org/abs/math/0501234

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arXiv