Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T07:44:55.779Z Has data issue: false hasContentIssue false
  • English
  • Français

Cyclic surgery on satellite knots

Published online by Cambridge University Press:  18 May 2009

Xingru Zhang
Xingru Zhang
Affiliation:
Mathematics Department, University of British Columbia, CanadaV6T 1Y4
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [9] L. Moser classified all manifolds obtained by Dehn surgery on torus knots. In particular she proved the following (see also [8, Chapter IV]).

Theorem 1 [9]. Nontrivial surgery with slope m/n on a nontrivial torus knot T(p, q) gives a manifold with cyclic fundamental group iff m = npq ± 1 and the manifold obtained is the lens space L(m, nq2).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 125 - 128
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Bailey, J. and Rolfsen, D., An unexpected surgery construction of a lens space. Pacific J. Math. 71 (1977), 295–298.CrossRefGoogle Scholar
2.Bleiler, S. and Litherland, R., Lens spaces and Dehn surgery, Proc. Amer. Math. Soc. 107 (1989), 1091–1094.CrossRefGoogle Scholar
3.Culler, M., Gordon, C., Luecke, J. and Shalen, P., Dehn surgery on knots, Ann. of Math. (2) 125 (1987), 237–300.CrossRefGoogle Scholar
4.Fintushel, R. and Stern, R., Constructing lens spaces by surgery on knots, Math. Z. 175 (1980), 33–51.CrossRefGoogle Scholar
5.Gabai, D., Surgery on knots in solid tori, Topology 28 (1989), 1–6.CrossRefGoogle Scholar
6.Gabai, D., 1-bridge braids in solid tori, preprint.Google Scholar
7.Gordon, C., Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983), 687–708.CrossRefGoogle Scholar
8.Jaco, W., Lectures on 3-manifold topology, Regional Conference Series in Mathematics 43 (A.M.S., 1980).CrossRefGoogle Scholar
9.Moser, L., Elementary surgery along a torus knot, Pacific J. Math. 38 (1971), 737–745.CrossRefGoogle Scholar
10.Scharlemann, M., Producing reducible 3-manifolds by surgery on a knot, preprint.Google Scholar
11.Wang, S., Cyclic surgery on knots, Proc. Amer. Math. Soc. 107 (1989), 1127–1131.CrossRefGoogle Scholar
12.Wu, Y., Cyclic surgery and satellite knots, preprint.Google Scholar