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)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Foliations of $ E(5\sb 2)$ and related knot complements


Authors: John Cantwell and Lawrence Conlon
Journal: Proc. Amer. Math. Soc. 118 (1993), 953-962
MSC: Primary 57R30; Secondary 57M25
DOI: https://doi.org/10.1090/S0002-9939-1993-1151808-5
MathSciNet review: 1151808
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The depth one foliations with a single compact leaf are classified for twist knots and pretzel knots $ (3, - 3,2n + 1)$.

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

  • [1] B. Burde and H. Zieschang, Knots, Stud. Math., vol. 5, de Gruyter, New York, 1985. MR 808776 (87b:57004)
  • [2] J. Cantwell and L. Conlon, Surgery and foliations of knot complements (to appear). MR 1247574 (94m:57055)
  • [3] -, Topological obstructions to smoothing proper foliations (in preparation).
  • [4] S. Fenley, Depth one foliations in hyperbolic $ 3$-manifolds, Ph.D. thesis, Princeton Univ., 1990.
  • [5] D. Gabai, Foliations and the topology of $ 3$-manifolds, J. Differential Geom. 18 (1983), 445-503. MR 723813 (86a:57009)
  • [6] -, Foliations and genera of links, Topology 23 (1984), 381-394. MR 780731 (86h:57006)
  • [7] -, Genera of the arborescent links, Mem. Amer. Math. Soc., vol. 59, Amer. Math. Soc., Providence, RI, 1986, pp. 1-98. MR 823442 (87h:57010)
  • [8] -, Foliations and the topology of $ 3$-manifolds. II, J. Differential Geom. 26 (1987), 461-478. MR 910017 (89a:57014a)
  • [9] -, Foliations and the topology of $ 3$-manifolds. III, J. Differential Geom. 26 (1987), 479-536. MR 910018 (89a:57014b)
  • [10] C. McA. Gordon and J. Leucke, Knots are determined by their complements, Bull. Amer. Math. Soc. (N.S.) 20 (1989), 83-87. MR 972070 (90a:57006b)
  • [11] John Harer, How to construct all fibered knots and links, Topology 21 (1982), 262-280. MR 649758 (83e:57007)
  • [12] D. Rolfsen, Knots and links, Publish or Perish, Berkeley, CA, 1976. MR 0515288 (58:24236)
  • [13] W. Thurston, A norm on the homology of three-manifolds, Mem. Amer. Math. Soc., vol. 59, Amer. Math. Soc., Providence, RI, 1986, 99-130. MR 823443 (88h:57014)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57R30, 57M25

Retrieve articles in all journals with MSC: 57R30, 57M25

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1151808-5
Keywords: Depth one foliation, taut, knot complement, Thurston norm
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society