International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 2, Pages 95-108
doi:10.1155/S0161171200003422
About some infinite family of 2-bridge knots and 3-manifolds
Department of Mathematics, Dongeui University, 24, Kaya Dong, Pusanjin-Ku, Pusan 614-714, Korea
Received 1 December 1998; Revised 12 March 1999
Copyright © 2000 Yangkok Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We construct an infinite family of 3-manifolds and show that these
manifolds have cyclically presented fundamental groups
and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots
(ℓ+1)2 or (ℓ+1)1, that are the closure
of the rational (2ℓ−1)/(ℓ−1)-tangles or
(2ℓ−1)/ℓ-tangles, respectively.