Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Isotopy types of knots of codimension two


Author: M. Š. Farber
Journal: Trans. Amer. Math. Soc. 261 (1980), 185-209
MSC: Primary 57Q45; Secondary 55P25
DOI: https://doi.org/10.1090/S0002-9947-1980-0576871-7
MathSciNet review: 576871
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the classification of n-dimensional knots in $ {S^{n + 2}}$, bounding r-connected manifolds, where $ 3r\, \geqslant \,n\, + \,1\, \geqslant \,6$, in terms of stable homotopy theory is suggested.


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

  • [1] G. E. Bredon, Regular O(n) manifolds, suspension of knots, and knot periodicity, Bull. Amer. Math. Soc. 79 (1973), 87-91. MR 0310901 (46:9999)
  • [2] M. Š. Farber, Classification of some knots of codimension two, Dokl. Akad. Nauk SSSR 240 (1978), 32-35; English transl., Soviet. Math. Dokl. 19 (1978). MR 0515702 (58:24280)
  • [3] J. F. P. Hudson, Embeddings of bounded manifolds, Proc. Cambridge Philos. Soc. 72 (1972), 11-20. MR 0298679 (45:7728)
  • [4] C. Kearton, Blanchfield duality and simple knots, Trans. Amer. Math. Soc. 202 (1975), 141-160. MR 0358796 (50:11255)
  • [5] -, An algebraic classification of some even-dimensional knots, Topology 15 (1976), 363-373. MR 0442948 (56:1323)
  • [6] R. Lashof and J. Shaneson, Classification of knots of codimension two, Bull. Amer. Math. Soc. 75 (1969), 171-175. MR 0242175 (39:3508)
  • [7] J. Levine, Unknotting spheres in codimension two, Topology 4 (1965), 9-16. MR 0179803 (31:4045)
  • [8] -, A classification of differentiable knots, Ann. of Math. (2) 82 (1965), 15-51. MR 0180981 (31:5211)
  • [9] -, Polynomial invariants of knots of codimension two, Ann. of Math. (2) 84 (1966), 537-554. MR 0200922 (34:808)
  • [10] -, An algebraic classification of some knots of codimension two, Comment. Math. Helv. 45 (1970), 185-198. MR 0266226 (42:1133)
  • [11] C. P. Rourke, Embedded handle theory, concordance and isotopy, Topology of Manifolds, Markham, Chicago, Ill., 1970. MR 0279816 (43:5537)
  • [12] H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1934), 571-592. MR 1512955
  • [13] E. H. Spanier, Function spaces and duality, Ann. of Math. (2) 70 (1959), 338-378. MR 0107862 (21:6584)
  • [14] -, Algebraic topology, McGraw-Hill, New York, 1966. MR 0210112 (35:1007)
  • [15] R. E. Stong, Notes on cobordism theory, Princeton Univ. Press, Princeton, N. J.; Univ. of Tokyo Press, Tokyo, 1968. MR 0248858 (40:2108)
  • [16] H. F. Trotter, On S-equivalence of Seifert matrices, Invent. Math. 20 (1973), 173-207. MR 0645546 (58:31100)
  • [17] C. T. C. Wall, Classification problems in differential topology-IV thickenings, Topology 5 (1966), 73-94. MR 0192509 (33:734)
  • [18] G. W. Whitehead, Recent advances in homotopy theory, CBMS Regional Conf. Ser. in Math., No. 5, Amer. Math. Soc., Providence, R. I., 1970. MR 0309097 (46:8208)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57Q45, 55P25

Retrieve articles in all journals with MSC: 57Q45, 55P25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0576871-7
Keywords: n-knot, Seifert manifold, homotopy pairing
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society