Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Finiteness of isotopy classes of certain knots

Author: Jean-Claude Hausmann
Journal: Proc. Amer. Math. Soc. 78 (1980), 417-423
MSC: Primary 57Q45
MathSciNet review: 553387
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove finiteness results for the isotopy classes of certain high-dimensional knots whose complement satisfies some homology conditions. In some particular cases, the isotopy class of a knot is determined by the twisted homology of its complement.

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

  • [Fu] L. Fuchs, Infinite abelian groups, Academic Press, New York and London, 1973. MR 0349869 (50:2362)
  • [Ha] J.-Cl. Hausmann, Noeuds antisimples. Knot theory, Proc. Conf. at Les-Plans-sur-Bex, 1977, Lecture Notes in Math., vol. 685, Springer-Verlag, Berlin and New York, pp. 171-202. MR 521733 (80j:57020)
  • [Hu] S. T. Hu, Homotopy theory, Academic Press, New York, 1959. MR 0106454 (21:5186)
  • [Ke] M. Kervaire, Les noeuds en dimensions supérieures, Bull. Soc. Math. France 93 (1965), 225-271. MR 0189052 (32:6479)
  • [Le] J. Levine, Knot modules. I, Trans. Amer. Math. Soc. 229 (1977), 1-50. MR 0461518 (57:1503)
  • [Su] D. Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. (2) 100 (1974), 1-79. MR 0442930 (56:1305)
  • [Sr] D. W. Sumners, Polynomial invariants and the integral homology of coverings of knots and links, Invent. Math. 15 (1972), 78-90. MR 0292062 (45:1150)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57Q45

Retrieve articles in all journals with MSC: 57Q45

Additional Information

Keywords: Knots, homotopy of Moore spaces
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society