On a group that cannot be the group of a $2$-knot
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- by Kunio Murasugi
- Proc. Amer. Math. Soc. 64 (1977), 154-156
- DOI: https://doi.org/10.1090/S0002-9939-1977-0440530-7
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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
- 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
Bibliographic 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