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Dehn surgeries on knots which yield lens spaces and genera of knots
https://hiroshima.repo.nii.ac.jp/records/2007684
https://hiroshima.repo.nii.ac.jp/records/200768474ea983c-efc5-49f9-a832-0dd19ada5828
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
Math-proc-Camb-Philos-Soc_129_3_501-515_2000.pdf (505.5 KB)
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| Item type | デフォルトアイテムタイプ_（フル）(1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2023-03-18 | |||||||||
| タイトル | ||||||||||
| タイトル | Dehn surgeries on knots which yield lens spaces and genera of knots | |||||||||
| 言語 | en | |||||||||
| 作成者 |
Goda, Hiroshi
× Goda, Hiroshi
× Teragaito, Masakazu
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| アクセス権 | ||||||||||
| アクセス権 | open access | |||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
| 権利情報 | ||||||||||
| 権利情報 | Copyright (c) 2000 Cambridge University Press | |||||||||
| 主題 | ||||||||||
| 主題Scheme | NDC | |||||||||
| 主題 | 410 | |||||||||
| 内容記述 | ||||||||||
| 内容記述 | 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 ([minus sign]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. | |||||||||
| 言語 | en | |||||||||
| 出版者 | ||||||||||
| 出版者 | Cambridge University Press | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | journal article | |||||||||
| 出版タイプ | ||||||||||
| 出版タイプ | VoR | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||
| 関連情報 | ||||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | 10.1017/S0305004100004692 | |||||||||
| 関連情報 | ||||||||||
| 関連タイプ | isVersionOf | |||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | http://dx.doi.org/10.1017/S0305004100004692 | |||||||||
| 収録物識別子 | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 0305-0041 | |||||||||
| 開始ページ | ||||||||||
| 開始ページ | 501 | |||||||||
| 書誌情報 |
Mathematical proceedings of the Cambridge Philosophical Society Mathematical proceedings of the Cambridge Philosophical Society 巻 129, 号 3, p. 501-515, 発行日 2000 |
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| 旧ID | 14107 | |||||||||
