Se p 20 01 Cyclic presentations of groups and branched cyclic coverings of ( 1 , 1
نویسنده
چکیده
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.
منابع مشابه
Ju n 20 01 The many faces of cyclic branched coverings of 2 - bridge knots and links ∗
We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, which are cyclic presentations in the case of 2-bridge knots. The homology gro...
متن کاملStrongly-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 کاملSTRONGLY-CYCLIC BRANCHED COVERINGS OF KNOTS VIA (g, 1)-DECOMPOSITIONS
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.
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 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 کامل