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Dehn surgeries on knots which yield lens spaces and genera of knots
| Content Provider | Scilit |
|---|---|
| Author | Goda, Hiroshi Teragaito, Masakazu |
| Copyright Year | 2000 |
| Description | It is an interesting open question when Dehn surgery on a knot in the 3-sphere S3 can produce a lens space (see [10, 12]). Some studies have been made for special knots; in particular, the question is completely solved for torus knots [21] and satellite knots [3, 29, 31]. It is known that there are many examples of hyperbolic knots which admit Dehn surgeries yielding lens spaces. For example, Fintushel and Stern [8] have shown that 18- and 19-surgeries on the (−2, 3, 7)-pretzel knot give lens spaces L(18, 5) and L(19, 7), respectively. However, there seems to be no essential progress on hyperbolic knots. It might be a reason that some famous classes of hyperbolic knots, such as 2-bridge knots [26], alternating knots [5], admit no surgery yielding lens spaces.In this paper we focus on the genera of knots to treat the present condition methodically and show that there is a constraint on the order of the fundamental group of the resulting lens space obtained by Dehn surgery on a hyperbolic knot. Also, this new standpoint enables us to present a conjecture concerning such a constraint, which holds for all known examples. |
| Related Links | http://arxiv.org/pdf/math/9902157 http://arxiv.org/abs/math/9902157 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7D30F0071CAE6DAFCD8044C4ACE8CF0F/S0305004100004692a.pdf/div-class-title-dehn-surgeries-on-knots-which-yield-lens-spaces-and-genera-of-knots-div.pdf |
| Ending Page | 515 |
| Page Count | 15 |
| Starting Page | 501 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100004692 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 129 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2000-11-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Yielding Lens Lens Spaces Genera of Knots Dehn Surgeries |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
