Examples of higher-dimensional slice knots which are not ribbon knots

Author:
L. R. Hitt

Journal:
Proc. Amer. Math. Soc. **77** (1979), 291-297

MSC:
Primary 57Q45

DOI:
https://doi.org/10.1090/S0002-9939-1979-0542100-0

MathSciNet review:
542100

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Abstract | References | Similar Articles | Additional Information

Abstract: A definition for ribbon *n*-knot is given which reduces to the previously studied definitions for and . It is shown that for each there is a slice *n*-knot which is not a ribbon *n*-knot.

**[F]**R. H. Fox,*A quick trip through knot theory*, Topology of 3-Manifolds and Related Topics, Prentice-Hall, Englewood Cliffs, N. J., 1961, pp. 120-167. MR**0140099 (25:3522)****[F]**-,*Some problems in knot theory*, Topology of 3-Manifolds and Related Topics, Prentice-Hall, Englewood Cliffs, N. J., pp. 168-176. MR**0140100 (25:3523)****[H]**L. R. Hitt,*Handlebody presentations of knot cobordisms*, Ph. D. Dissertation, Florida State University, 1977.**[H]**-,*Ribbon n-knots*, preprint, University of South Alabama.**[K]**M. A. Kervaire,*Les noeuds de dimensions supérieures*, Bull. Soc. Math. France**93**(1965), 225-271. MR**0189052 (32:6479)****[L]**J. Levine,*Polynomial invariants of knots of codimension two*, Ann. of Math. (2)**84**(1966), 537-554. MR**0200922 (34:808)****[M]**J. Milnor,*Infinite cyclic coverings*, Conference on the Topology of Manifolds, Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 115-133. MR**0242163 (39:3497)****[R]**D. Roseman,*Ribbon knots*, preprint, University of Iowa.**[Sc]**H. Schubert,*Knoten mit zwei Brücken*, Math. Z.**65**(1950), 133-170. MR**0082104 (18:498e)****[SS]**Y. Shinohara and D. W. Sumners,*Homology invariants of cyclic coverings with applications to links*, Trans. Amer. Math. Soc.**163**(1972), 101-121. MR**0284999 (44:2223)****[S]**D. W. Sumners,*of the commutator subgroup of a knot group*, Proc. Amer. Math. Soc.**28**(1971), 319-320. MR**0275416 (43:1173)****[S]**-,*The effect of spinning and twist spinning on some knot invariants*, preprint, Florida State University.**[Yaj]**T. Yajima,*On simply knotted spheres in*, Osaka J. Math.**1**(1964), 133-152. MR**0172280 (30:2500)****[Yan]**T. Yanagawa,*On ribbon*2-*knots, the*3-*manifold bounded by the*2-*knots*, Osaka J. Math.**6**(1969), 447-464. MR**0266193 (42:1101)****[Z]**E. C. Zeeman,*Twisting spun knots*, Trans. Amer. Math. Soc.**115**(1965), 471-495. MR**0195085 (33:3290)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0542100-0

Keywords:
Ribbon knot,
slice knot,
infinite cyclic covering space,
knot cobordism

Article copyright:
© Copyright 1979
American Mathematical Society