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 manifold...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/573403 |
| 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
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). |
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| ISSN: | 0161-1712 1687-0425 |