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Transactions of the American Mathematical Society

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On higher-dimensional fibered knots


Authors: J. J. Andrews and D. W. Sumners
Journal: Trans. Amer. Math. Soc. 153 (1971), 415-426
MSC: Primary 55.20
DOI: https://doi.org/10.1090/S0002-9947-1971-0271927-5
MathSciNet review: 0271927
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Abstract: The geometrical properties of a fibration of a knot complement over $ {S^1}$ are used to develop presentations for the homotopy groups as modules over the fundamental group. Some homotopy groups of spun and twist-spun knots are calculated.


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

  • [1] J. J. Andrews and M. L. Curtis, Knotted $ 2$-spheres in the $ 4$-sphere, Ann. of Math. (2) 70 (1959), 565-571. MR 21 #5964. MR 0107239 (21:5964)
  • [2] J. J. Andrews and S. J. Lomonaco, The second homotopy group of spun $ 2$-spheres in $ 4$-space, Bull. Amer. Math. Soc. 75 (1969), 169-171. MR 38 #3863. MR 0235559 (38:3863)
  • [3] W. Browder and J. Levine, Fibering manifolds over a circle, Comment. Math. Helv. 40 (1966), 153-160. MR 33 #3309. MR 0195104 (33:3309)
  • [4] D. B. A. Epstein, Linking spheres, Proc. Cambridge Philos. Soc. 56 (1960), 215-219. MR 22 #8514. MR 0117740 (22:8514)
  • [5] F. T. Farrell, The obstruction to fibering a manifold over a circle, Ph.D. Thesis, Yale University, New Haven, Conn., 1968. MR 0215310 (35:6151)
  • [6] E. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)
  • [7] E. C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965), 471-495. MR 33 #3290. MR 0195085 (33:3290)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0271927-5
Keywords: Fibered knots, twist-spun knots, module structure of homotopy groups
Article copyright: © Copyright 1971 American Mathematical Society

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