Abstract
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 Ld+1 of d + 1 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
Summary
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
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