Article
| Title: | A note on rational surgeries on a Hopf link (English) |
| Author: | Bojković, Velibor |
| Author: | Nikolić, Jovana |
| Author: | Zekić, Mladen |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 603-611 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | It is clear that every rational surgery on a Hopf link in $3$-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the $3$-sphere. (English) |
| Keyword: | continued fraction |
| Keyword: | Hopf link |
| Keyword: | lens space |
| Keyword: | rational surgery |
| Keyword: | Rolfsen moves |
| MSC: | 11A55 |
| MSC: | 57K30 |
| MSC: | 57R65 |
| idZBL: | Zbl 07729526 |
| idMR: | MR4586913 |
| DOI: | 10.21136/CMJ.2023.0144-22 |
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| Date available: | 2023-05-04T17:51:08Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151676 |
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| Reference: | [2] Gompf, R. E., Stipsicz, A. I.: 4-Manifolfs and Kirby Calculus.Graduate Studies in Mathematics 20. AMS, Providence (1999). Zbl 0933.57020, MR 1707327, 10.1090/gsm/020 |
| Reference: | [3] Khinchin, A. Y.: Continued Fractions.The University of Chicago Press, Chicago (1964). Zbl 0117.28601, MR 0161833 |
| Reference: | [4] Kirby, R.: A calculus for framed links in $S^3$.Invent. Math. 45 (1978), 35-56. Zbl 0377.55001, MR 0467753, 10.1007/BF01406222 |
| Reference: | [5] Prasolov, V. V., Sossinsky, A. B.: Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology.Translations of Mathematical Monographs 154. AMS, Providence (1997). Zbl 0864.57002, MR 1414898, 10.1090/mmono/154 |
| Reference: | [6] Rolfsen, D.: Knots and Links.Mathematical Lecture Series 7. Publish or Perish, Berkeley (1976). Zbl 0339.55004, MR 0515288 |
| Reference: | [7] Rolfsen, D.: Rational surgery calculus: Extension of Kirby's theorem.Pac. J. Math. 110 (1984), 377-386. Zbl 0488.57002, MR 0726496, 10.2140/pjm.1984.110.377 |
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