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

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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.

**1.**David Gabai,*The Murasugi sum is a natural geometric operation*, Low-dimensional topology (San Francisco, Calif., 1981) Contemp. Math., vol. 20, Amer. Math. Soc., Providence, RI, 1983, pp. 131–143. MR**718138**, 10.1090/conm/020/718138**2.**Charles Livingston and Paul Melvin,*Algebraic knots are algebraically dependent*, Proc. Amer. Math. Soc.**87**(1983), no. 1, 179–180. MR**677257**, 10.1090/S0002-9939-1983-0677257-5**3.**Katura Miyazaki,*Nonsimple, ribbon fibered knots*, Trans. Amer. Math. Soc.**341**(1994), no. 1, 1–44. MR**1176509**, 10.1090/S0002-9947-1994-1176509-4**4.**Walter Neumann and Lee Rudolph,*Unfoldings in knot theory*, Math. Ann.**278**(1987), no. 1-4, 409–439. MR**909235**, 10.1007/BF01458078**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) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 55–60. MR**520522**

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Additional Information

**Lee Rudolph**

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

Email:
lrudolph@black.clarku.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06520-6

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

Published electronically:
April 22, 2002

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 2002
American Mathematical Society