Academic Editor: S. M. Gusein-Zade
Copyright © 2010 Soo Hwan Kim and 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.
We study the algebraic and geometric structures for
closed orientable -manifolds obtained by Dehn surgery along the family of
hyperbolic links with certain surgery coefficients and
moreover, the geometric presentations of the fundamental group of these manifolds.
We prove that our surgery manifolds are -fold cyclic covering of -sphere
branched over certain link by applying the Montesinos theorem in Montesinos-Amilibia (1975).
In particular, our result includes the topological classification of the closed -manifolds
obtained by Dehn surgery on the Whitehead link, according to Mednykh and Vesnin (1998), and
the hyperbolic link of components in Cavicchioli and Paoluzzi (2000).