2003/09/18 by Alessia Cattabriga, Cattabriga, Alessia, Michele Mulazzani +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Connective tissue disorders research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M12 #msc:57M25 #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/0309298
22 pages, 19 figures. Revised version with minor changes in Proposition 5. Accepted for publication in the Journal of the London Mathematical Society
arxiv created 2004/03/04 · arxiv updated 2009/12/01
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.