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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a group that cannot be the group of a $2$-knot
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by Kunio Murasugi PDF
Proc. Amer. Math. Soc. 64 (1977), 154-156 Request permission

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
  • H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957. MR 0088489
  • 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
  • Heinz Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257–309 (German). MR 6510, DOI 10.1007/BF02565622
  • 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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 154-156
  • MSC: Primary 55A25
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0440530-7
  • MathSciNet review: 0440530