Abstract

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).

Highlights

  • Soo Hwan Kim and Yangkok KimWe 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 the geometric presentations of the fundamental group of these manifolds

  • All manifolds will be assumed to be connected, orientable, and PL Piecewise Linear

  • 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 the geometric presentations of the fundamental group of these manifolds

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Summary

Soo Hwan Kim and Yangkok Kim

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 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. 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 Ld 1 of d 1 components in Cavicchioli and Paoluzzi 2000

Introduction
International Journal of Mathematics and Mathematical Sciences
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