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Transactions of the American Mathematical Society

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On the Seifert manifold of a $ 2$-knot


Author: M. A. Gutierrez
Journal: Trans. Amer. Math. Soc. 240 (1978), 287-294
MSC: Primary 57C45
DOI: https://doi.org/10.1090/S0002-9947-1978-0482778-7
MathSciNet review: 0482778
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Abstract: From geometric facts about embeddings $ {S^2} \to {S^4}$ we study the relationship between the smallest number of normal generators (weight) of a group and its preabelian presentations.


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

  • [1] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956. MR 0077480 (17:1040e)
  • [2] M. Gutierrez, Homology of knot groups. I, Bol. Soc. Mat. Mexicana 16 (1971), 58-63. MR 0336751 (49:1524)
  • [3] -, Homology of knot groups. II (to appear).
  • [4] -, An exact sequence for the second homology of a knot, Proc. Amer. Math. Soc. 32 (1972), 571-577. MR 0322848 (48:1209)
  • [5] M. Kervaire, On higher dimensional knots, in Combinatorial and Differential Topology, Princeton Univ. Press, Princeton, N.J., 1962. MR 0178475 (31:2732)
  • [6] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.
  • [7] L. Newwirth, Knot groups, Ann. of Math. Studies, no. 56, Princeton Univ. Press, Princeton, N.J., 1965.
  • [8] J. Stallings, On torsion free groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312-324. MR 0228573 (37:4153)
  • [9] 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/S0002-9947-1978-0482778-7
Keywords: Seifert manifolds, iterated free product with amalgamation
Article copyright: © Copyright 1978 American Mathematical Society

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