Geodesic
A note on rational surgeries on a Hopf link
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 603-611
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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.
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.
DOI : 10.21136/CMJ.2023.0144-22
Classification : 11A55, 57K30, 57R65
Keywords: continued fraction; Hopf link; lens space; rational surgery; Rolfsen moves 
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Bojković, Velibor; Nikolić, Jovana; Zekić, Mladen. A note on rational surgeries on a Hopf link. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 603-611. doi: 10.21136/CMJ.2023.0144-22

[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. | DOI | MR | JFM

[2] Gompf, R. E., Stipsicz, A. I.: 4-Manifolfs and Kirby Calculus. Graduate Studies in Mathematics 20. AMS, Providence (1999). | DOI | MR | JFM

[3] Khinchin, A. Y.: Continued Fractions. The University of Chicago Press, Chicago (1964). | MR | JFM

[4] Kirby, R.: A calculus for framed links in $S^3$. Invent. Math. 45 (1978), 35-56. | DOI | MR | JFM

[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). | DOI | MR | JFM

[6] Rolfsen, D.: Knots and Links. Mathematical Lecture Series 7. Publish or Perish, Berkeley (1976). | MR | JFM

[7] Rolfsen, D.: Rational surgery calculus: Extension of Kirby's theorem. Pac. J. Math. 110 (1984), 377-386. | DOI | MR | JFM

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