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A non-ribbon plumbing of fibered ribbon knots
Author(s):
Lee
Rudolph
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3741-3743.
MSC (2000):
Primary 57M25
Posted:
April 22, 2002
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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:
-
- 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
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Additional Information:
Lee
Rudolph
Affiliation:
Department of Mathematics, Clark University, Worcester, Massachusetts 01610
Email:
lrudolph@black.clarku.edu
DOI:
10.1090/S0002-9939-02-06520-6
PII:
S 0002-9939(02)06520-6
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
Posted:
April 22, 2002
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2002,
American Mathematical Society
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