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EnglishWe 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 in the 3-sphere.
| Titolo: | All strongly-cyclic branched coverings of (1,1)-knots are Dunwoody manifolds |
| Autore/i: | CATTABRIGA, ALESSIA; MULAZZANI, MICHELE |
| Autore/i Unibo: | |
| Anno: | 2004 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1112/S0024610704005538 |
| 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 in the 3-sphere. |
| Data prodotto definitivo in UGOV: | 2005-10-10 15:55:30 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/12872
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