All strongly-cyclic branched coverings of (1,1)-knots are Dunwoody manifolds

Alessia Cattabriga; Michele Mulazzani

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arXiv · math/0309298

All strongly-cyclic branched coverings of (1,1)-knots are Dunwoody manifolds

Alessia Cattabriga·Michele Mulazzani

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Abstract

We show that every strongly-cyclic branched covering of a (1,1)-knot is a Dunwoody manifold. This result, together with the converse statement previously obtained by Grasselli and Mulazzani, proves that the class of Dunwoody manifolds coincides with the class of strongly-cyclic branched coverings of (1,1)-knots. As a consequence, we obtain a parametrization of (1,1)-knots by 4-tuples of integers. Moreover, using a representation of (1,1)-knots by the mapping class group of the twice punctured torus, we provide an algorithm which gives the parametrization of all torus knots.

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BibTeX RIS

Alessia Cattabriga, Michele Mulazzani. 2004-03-04. All strongly-cyclic branched coverings of (1,1)-knots are Dunwoody manifolds. https://arxiv.org/abs/math/0309298

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