Dehn surgeries on strongly invertible knots which yield lens spaces

Proceedings of the American Mathematical Society

Volumn 128, Issue 11, 2000, Pages 3445-3451

  Hirasawa, Mikami ^a   Shimokawa, Koya ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

Banding; Dehn surgery; Lens space; Strongly invertible knot

Indexed keywords

EID: 0347113895     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-00-05417-4     Document Type: Article

References (19)

1. J. Berge, Some knots with surgeries yielding lens spaces., preprint.
2. S. Bleiler, Prime tangles and composite knots., In Knot theory and manifolds, Lecture Note in Math. vol. 1144, pp. 1-13 (Springer-Verlag 1983) MR 87e:57006
3. S. Bleiler and R. Litherland, Lens space and Dehn surgery., Proc. Amer. Math. Soc. vol. 107 (1989) 1127-1131. MR 90e:57031
4. 4 with three critical points is standard. Strongly invertible knots have property P., Topology vol. 27 (1988) 519-540. MR 90e:57006
5. M. Culler, C. McA. Gordon, J. Luecke and P. B. Shalen, Dehn surgery on knots. Ann. of Math. vol. 125 (1987) 237-300. MR 88a:57026
6. D. Gabai, Foliations and the topology of 3-manifolds II., J. Diff. Geom. vol. 26 (1987) 461-478. MR 89a:57014a
7. Foliations and the topology of 3-manifolds III., J. Diff. Geom. vol. 26 (1987) 479-536. MR 89a:57014b
8. C. Hodgson and H. Rubinstein, Involutions and isotopies of lens spaces., In Knot theory and manifolds, Lecture Note in Math. vol. 1144 pp. 60-96 (Springer-Verlag 1983) MR 87h:57028
9. R. Kirby ed., Problems in low-dimensional topology., In Geometric Topology, Part 2, Studies in Advanced Mathematics pp. 34-173, (AMS/IP 1997) CMP 98:01
10. T. Kobayashi, Uniqueness of minimal genus Seifert surfaces for links., Topology Appl. vol. 33 (1989) 265-279. MR 91c:57009
11. n without fixed points., Amer. J. Math. vol. 79 (1957) 623-631. MR 19:761d
12. 3., In Knots, groups and 3-manifolds, Ann. of Math. Studies vol. 84 pp. 227-259 (Princeton University Press 1975) MR 52:1699
13. L. Moser, Elementary surgery along a torus knot., Pacific J. Math. vol. 38 (1971) 737-745. MR 52:4287
14. K. Murasugi, On a certain numerical invariant of link types., Trans. Amer. Math. Soc. vol. 117 (1965) 387-422.
15. M. Scharlemann and A. Thompson, Link genus and Conway moves., Comm. Math. Helv. vol. 64 (1989) 527-535. MR 91b:57006
16. A. Thompson, Knots with unknotting number one are determined by their complements., Topology vol. 28 (1989) 225-230. MR 90f:57011
17. W. Thurston, Three-manifold with symmetry., preprint.
18. F. Waldhausen, Über Involutionen der 3-Sphäre., Topology vol. 8 (1969) 81-91. MR 38:5209
19. S. Wang and Q. Zhou, Symmetry of knots and cyclic surgery., Trans. Amer. Math. Soc. vol. 330 (1992) 665-676. MR 92f:57017