STRONGLY-CYCLIC BRANCHED COVERINGS OF KNOTS VIA (g, 1)-DECOMPOSITIONS
نویسنده
چکیده
Strongly-cyclic branched coverings of knots are studied by using their (g, 1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations.
منابع مشابه
Strongly-cyclic branched coverings of (1,1)-knots and cyclic presentations of groups
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold stronglycyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold stro...
متن کاملar X iv : m at h / 04 02 39 3 v 1 [ m at h . G T ] 2 4 Fe b 20 04 CYCLIC BRANCHED COVERINGS OF ( g , 1 ) - KNOTS
We study (g, 1)-knots and their strongly-cyclic branched coverings, proving the necessary and sufficient conditions for their existence and uniqueness, and characterizing their fundamental groups. As a relevant example, we prove that generalized periodic Takahashi manifolds belong to this family of manifolds.
متن کاملO ct 2 00 1 Strongly - cyclic branched coverings of ( 1 , 1 ) - knots and cyclic presentations of groups ∗
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold stronglycyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold stro...
متن کاملSe p 20 01 Cyclic presentations of groups and branched cyclic coverings of ( 1 , 1
In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1, 1)-knots. In particular , we prove that every n-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.
متن کاملAll strongly-cyclic branched coverings of (1, 1)-knots are Dunwoody manifolds
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 stronglycyclic branched coverings of (1, 1)-knots. As a consequence, we obtain a parametrization of (1, 1)-knots by 4-tuples of intege...
متن کامل