Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Lens spaces and Dehn surgery

Authors: Steven A. Bleiler and Richard A. Litherland
Journal: Proc. Amer. Math. Soc. 107 (1989), 1127-1131
MSC: Primary 57N10; Secondary 57M25
MathSciNet review: 984783
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The question of when a lens space arises by Dehn surgery is discussed with a characterization given for satellite knots. The lens space $ L\left( {2,1} \right)$, i.e. real projective $ 3$-space, is shown to be unobtainable by surgery on a symmetric knot.

References [Enhancements On Off] (What's this?)

  • [BR] J. Bailey and D. Rolfsen, An unexpected surgery construction of a lens space, Pacific J. Math. 71 (1977), 295-298. MR 0488061 (58:7633)
  • [B] S. A. Bleiler, Prime tangles and composite knots, Lecture Notes in Math. 1144, 1-13. MR 823278 (87e:57006)
  • [CGLS] M. Culler, C. Gordon, J. Luecke, and P. Shalen, Dehn surgery on knots, Ann. of Math. (2), 125 (1987), 237-300. MR 881270 (88a:57026)
  • [FS] R. Fintushel and R. Stern, Constructing lens spaces by surgery on knots, Math. Z. 175 (1980), 33-51. MR 595630 (82i:57009a)
  • [Ga] D. Gabai, Dehn surgery on knots in solid tori, preprint. MR 991095 (90h:57005)
  • [Go] C. McA. Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983), 687-708. MR 682725 (84d:57003)
  • [H] J. Hempel, Dehn fillings of coverings of surface bundles, Topology Appl. 24 (1986), 63-70. MR 872487 (88h:57011)
  • [HR] C. Hodgson and H. Rubinstein, Involutions and isotopies of lens spaces, Lecture Notes in Math. 1144, 60-96. MR 823282 (87h:57028)
  • [M] J. Montesinos, Surgery on links and double branched covers of $ {S^3}$, Ann. of Math. Stud. 84 (1975) 227-260. MR 0380802 (52:1699)
  • [Mo] L. Moser, Elementary surgery along torus knots, Pacific J. Math. 38 (1971), 734-745. MR 0383406 (52:4287)
  • [S] M. Scharlemann, Sutured manifolds and generalised Thurston norms, preprint. MR 992331 (90e:57021)
  • [T] A. Thompson, Unknotting number one knots are determined by their complements, preprint.
  • [Wa$ _{1}$] S. Wang, Cyclic surgery on knots, preprint.
  • [Wa$ _{2}$] -, Symmetry of knots against cyclic surgery, preprint.
  • [Wu] Wu, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10, 57M25

Retrieve articles in all journals with MSC: 57N10, 57M25

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society