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)



A non-ribbon plumbing of fibered ribbon knots

Author: Lee Rudolph
Journal: Proc. Amer. Math. Soc. 130 (2002), 3741-3743
MSC (2000): Primary 57M25
Published electronically: April 22, 2002
MathSciNet review: 1920056
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A closer look at an example introduced by Livingston and Melvin and later studied by Miyazaki shows that a plumbing of two fibered ribbon knots (along their fiber surfaces) may be algebraically slice yet not ribbon.

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

  • 1. David Gabai, The Murasugi sum is a natural geometric operation, Low-dimensional topology (San Francisco, Calif., 1981), Amer. Math. Soc., Providence, R.I., 1983, pp. 131-143. MR 85d:57003
  • 2. Charles Livingston and Paul Melvin, Algebraic knots are algebraically dependent, Proc. Amer. Math. Soc. 87 (1983), no. 1, 179-180. MR 84a:57004
  • 3. Katura Miyazaki, Nonsimple, ribbon fibered knots, Trans. Amer. Math. Soc. 341 (1994), no. 1, 1-44. MR 94c:57013
  • 4. Walter Neumann and Lee Rudolph, Unfoldings in knot theory, Math. Ann. 278 (1987), no. 1-4, 409-439. MR 89j:57017a
  • 5. Lee Rudolph, Query, Notices Amer. Math. Soc. 23 (1976), 410, in problem list compiled at the Special Session on Knot Theory, 1976 Summer Meeting of A.M.S., Toronto.
  • 6. John R. Stallings, Constructions of fibred knots and links, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2, Amer. Math. Soc., Providence, R.I., 1978, pp. 55-60. MR 80e:57004

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M25

Retrieve articles in all journals with MSC (2000): 57M25

Additional Information

Lee Rudolph
Affiliation: Department of Mathematics, Clark University, Worcester, Massachusetts 01610

Keywords: Fibered knot, Murasugi sum, plumbing, ribbon knot
Received by editor(s): July 16, 2001
Received by editor(s) in revised form: August 1, 2001
Published electronically: April 22, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society