Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a group that cannot be the group of a $ 2$-knot

Author: Kunio Murasugi
Journal: Proc. Amer. Math. Soc. 64 (1977), 154-156
MSC: Primary 55A25
MathSciNet review: 0440530
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Abstract: It is proved that a homomorph of the group of trefoil knot cannot be the group of a 2-knot in 4-sphere.

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

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  • [2] R. H. Fox, Some problems in knot theory, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 168–176. MR 0140100
  • [3] Heinz Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257–309 (German). MR 0006510
  • [4] Michel A. Kervaire, On higher dimensional knots, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 105–119. MR 0178475

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Keywords: n-knot, knot group
Article copyright: © Copyright 1977 American Mathematical Society