Representations of (1,1)-knots

Alessia Cattabriga; Michele Mulazzani

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arXiv · math/0501234

Representations of (1,1)-knots

Alessia Cattabriga·Michele Mulazzani

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Abstract

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.

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BibTeX RIS

Alessia Cattabriga, Michele Mulazzani. 2005-10-24. Representations of (1,1)-knots. https://arxiv.org/abs/math/0501234

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