| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-05-04T17:51:08Z |
| Last updated:
|
2025-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151676 |
| . |
| Reference:
|
[1] Cochran, T. D., Gompf, R. E.: Applications of Donaldson's theorems to classical knot concordance, homology 3-spheres and property $P$.Topology 27 (1988), 495-512. Zbl 0669.57003, MR 0976591, 10.1016/0040-9383(88)90028-6 |
| 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 |
| . |
