Isotopy types of knots of codimension two
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- by M. Š. Farber
- Trans. Amer. Math. Soc. 261 (1980), 185-209
- DOI: https://doi.org/10.1090/S0002-9947-1980-0576871-7
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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
- Glen E. Bredon, Regular $\textbf {O}(n)$-manifolds, suspension of knots, and knot periodicity, Bull. Amer. Math. Soc. 79 (1973), 87–91. MR 310901, DOI 10.1090/S0002-9904-1973-13105-2
- M. Š. Farber, Classification of certain knots of codimension two, Dokl. Akad. Nauk SSSR 240 (1978), no. 1, 32–35 (Russian). MR 0515702
- J. F. P. Hudson, Embeddings of bounded manifolds, Proc. Cambridge Philos. Soc. 72 (1972), 11–20. MR 298679, DOI 10.1017/s0305004100050908
- C. Kearton, Blanchfield duality and simple knots, Trans. Amer. Math. Soc. 202 (1975), 141–160. MR 358796, DOI 10.1090/S0002-9947-1975-0358796-3
- C. Kearton, An algebraic classification of some even-dimensional knots, Topology 15 (1976), no. 4, 363–373. MR 442948, DOI 10.1016/0040-9383(76)90030-6
- Richard K. Lashof and Julius L. Shaneson, Classification of knots in codimension two, Bull. Amer. Math. Soc. 75 (1969), 171–175. MR 242175, DOI 10.1090/S0002-9904-1969-12197-X
- J. Levine, Unknotting spheres in codimension two, Topology 4 (1965), 9–16. MR 179803, DOI 10.1016/0040-9383(65)90045-5
- J. Levine, A classification of differentiable knots, Ann. of Math. (2) 82 (1965), 15–50. MR 180981, DOI 10.2307/1970561
- J. Levine, Polynomial invariants of knots of codimension two, Ann. of Math. (2) 84 (1966), 537–554. MR 200922, DOI 10.2307/1970459
- J. Levine, An algebraic classification of some knots of codimension two, Comment. Math. Helv. 45 (1970), 185–198. MR 266226, DOI 10.1007/BF02567325
- C. P. Rourke, Embedded handle theory, concordance and isotopy, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp. 431–438. MR 0279816
- H. Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935), no. 1, 571–592 (German). MR 1512955, DOI 10.1007/BF01448044
- E. H. Spanier, Function spaces and duality, Ann. of Math. (2) 70 (1959), 338–378. MR 107862, DOI 10.2307/1970107
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
- Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
- H. F. Trotter, On $S$-equivalence of Seifert matrices, Invent. Math. 20 (1973), 173–207. MR 645546, DOI 10.1007/BF01394094
- C. T. C. Wall, Classification problems in differential topology. IV. Thickenings, Topology 5 (1966), 73–94. MR 192509, DOI 10.1016/0040-9383(66)90005-X
- George W. Whitehead, Recent advances in homotopy theory, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 5, American Mathematical Society, Providence, R.I., 1970. MR 0309097
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- 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