On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links

We study the algebraic and geometric structures for closed orientable 3 -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 2 -fold cyclic covering of 3 -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 3 -manifolds obtained by Dehn surgery on the Whitehead link, according to Mednykh and Vesnin (1998), and the hyperbolic link 𝐿 𝑑 + 1 of 𝑑 + 1 components in Cavicchioli and Paoluzzi (2000).