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...
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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 |
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doaj-69fb4485d28145798ad19462595a9c9d2020-11-24T22:31:16ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/573403573403On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on LinksSoo Hwan Kim0Yangkok Kim1Department of Mathematics, Doneeui University, Pusan 614-714, Republic of KoreaDepartment of Mathematics, Doneeui University, Pusan 614-714, Republic of KoreaWe 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).http://dx.doi.org/10.1155/2010/573403 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Soo Hwan Kim Yangkok Kim |
| spellingShingle |
Soo Hwan Kim Yangkok Kim On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Soo Hwan Kim Yangkok Kim |
| author_sort |
Soo Hwan Kim |
| title |
On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links |
| title_short |
On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links |
| title_full |
On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links |
| title_fullStr |
On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links |
| title_full_unstemmed |
On Hyperbolic 3-Manifolds Obtained by Dehn Surgery on Links |
| title_sort |
on hyperbolic 3-manifolds obtained by dehn surgery on links |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2010-01-01 |
| description |
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). |
| url |
http://dx.doi.org/10.1155/2010/573403 |
| work_keys_str_mv |
AT soohwankim onhyperbolic3manifoldsobtainedbydehnsurgeryonlinks AT yangkokkim onhyperbolic3manifoldsobtainedbydehnsurgeryonlinks |
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1725737961220210688 |