An algebraic classification of some even-dimensional spherical knots. I
HTML articles powered by AMS MathViewer
- by M. Š. Farber
- Trans. Amer. Math. Soc. 281 (1984), 507-527
- DOI: https://doi.org/10.1090/S0002-9947-1984-99927-2
- PDF | Request permission
Part II: Trans. Amer. Math. Soc. (2) (1984), 529-570
Abstract:
The main result of the paper is the classification of simple even-dimensional spherical knots in terms of their algebraic invariants.References
- Albrecht Dold and Dieter Puppe, Duality, trace, and transfer, Proceedings of the International Conference on Geometric Topology (Warsaw, 1978) PWN, Warsaw, 1980, pp. 81–102. MR 656721
- David A. Edwards and Ross Geoghegan, The Wall obstruction in shape and pro-homotopy, with applications, Bull. Amer. Math. Soc. 81 (1975), no. 5, 919–920. MR 375331, DOI 10.1090/S0002-9904-1975-13886-9
- M. Š. Farber, Linking coefficients and two-dimensional knots, Dokl. Akad. Nauk SSSR 222 (1975), no. 2, 299–301 (Russian). MR 0400246
- M. Š. Farber, Duality in an infinite cyclic covering, and even-dimensional knots, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), no. 4, 794–828, 959 (Russian). MR 0515677
- M. Š. Farber, Classification of certain knots of codimension two, Dokl. Akad. Nauk SSSR 240 (1978), no. 1, 32–35 (Russian). MR 0515702
- M. Š. Farber, Classification of certain multidimensional knots of codimension two, Uspekhi Mat. Nauk 35 (1980), no. 3(213), 105–111 (Russian). International Topology Conference (Moscow State Univ., Moscow, 1979). MR 580626
- M. Š. Farber, Isotopy types of knots of codimension two, Trans. Amer. Math. Soc. 261 (1980), no. 1, 185–209. MR 576871, DOI 10.1090/S0002-9947-1980-0576871-7
- M. Sh. Farber, Classification of stable fibred knots, Mat. Sb. (N.S.) 115(157) (1981), no. 2, 223–262, 319 (Russian). MR 622146
- Peter Freyd, Splitting homotopy idempotents, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 173–176. MR 0206069
- 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
- Sadayoshi Kojima, A classification of some even dimensional fibered knots, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), no. 3, 671–683. MR 645407
- Sadayoshi Kojima, Classification of simple knots by Levine pairings, Comment. Math. Helv. 54 (1979), no. 3, 356–367. MR 543336, DOI 10.1007/BF02566280
- J. Levine, An algebraic classification of some knots of codimension two, Comment. Math. Helv. 45 (1970), 185–198. MR 266226, DOI 10.1007/BF02567325
- Jerome Levine, Knot modules, Knots, groups, and $3$-manifolds (Papers dedicated to the memory of R. H. Fox), Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 25–34. MR 0405437
- Jerome Levine, Knot modules. I, Trans. Amer. Math. Soc. 229 (1977), 1–50. MR 461518, DOI 10.1090/S0002-9947-1977-0461518-0
- Saunders Mac Lane, Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR 1344215
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
- E. H. Spanier, Function spaces and duality, Ann. of Math. (2) 70 (1959), 338–378. MR 107862, DOI 10.2307/1970107
- H. F. Trotter, On $S$-equivalence of Seifert matrices, Invent. Math. 20 (1973), 173–207. MR 645546, DOI 10.1007/BF01394094
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 281 (1984), 507-527
- MSC: Primary 57Q45; Secondary 55P15
- DOI: https://doi.org/10.1090/S0002-9947-1984-99927-2
- MathSciNet review: 722762