| タイトル | Cosmetic surgery and the SL(2, C) Casson invariant for two-bridge knots |
| 著者（日） | 市原, 一裕; 斎藤, 敏夫 |
| 著者（英） | Ichihara, Kazuhiro; Saito, Toshio |
| 著者所属（日） | 日本大学; 上越教育大学 |
| 著者所属（英） | Nihon University; Joetsu University of Education |
| 発行日 | 2018-03 |
| 発行機関など | Department of Mathematics, Graduate School of Science, Hiroshima University
広島大学大学院理学研究科 |
| 刊行物名 | Hiroshima mathematical journal |
| 巻 | 48 |
| 号 | 1 |
| 開始ページ | 21 |
| 終了ページ | 37 |
| 刊行年月日 | 2018-03 |
| 言語 | eng |
| 抄録 | We consider the cosmetic surgery problem for two-bridge knots in the 3-sphere. We first verify by using previously known results that all the two-bridge knots of at most 9 crossings admit no purely cosmetic surgery pairs except for the knot 9(sub 27). Then we show that any two-bridge knot corresponding to the continued fraction brackets 0, 2x, 2, -2x, 2x, 2, -2x brackets for a positive integer x admits no cosmetic surgery pairs yielding homology 3-spheres, where 9(sub 27) appears when x = 1. Our advantage to prove this is using the SL(2,C) Casson invariant. |
| 内容記述 | Physical characteristics: Original contains illustrations
形態: 図版あり |
| キーワード | cosmetic surgery; SL(2, C) Casson invariant; two-bridge knot |
| 資料種別 | Journal Article |
| NASA分類 | Theoretical Mathematics |
| ISSN | 0018-2079 |
| NCID | AA00664323 |
| SHI-NO | AA1740412002 |
| URI | https://repository.exst.jaxa.jp/dspace/handle/a-is/883474 |
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