An algebraic classification of some even-dimensional spherical knots. II
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- by M. Š. Farber PDF
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Abstract:
The paper reduces the problem of classification of simple even-dimensional spherical knots of codimension two to an algebraic problem.References
- M. Š. Farber, An algebraic classification of some even-dimensional spherical knots. I, II, Trans. Amer. Math. Soc. 281 (1984), no. 2, 507–527, 529–570. MR 722762, DOI 10.1090/S0002-9947-1984-99927-2
- 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. 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. Sh. Farber, Presentations of knot modules, Izv. Akad. Nauk Azerbaĭdzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk 2 (1981), no. 2, 105–111 (Russian, with English and Azerbaijani summaries). MR 634183 —, Functors in the category of knot modules, Izv. Akad. Nauk Azerbaǐdzhan SSR Ser. Fiz.-Tekhn Mat. Nauk 3 (1981), 95-101. (Russian)
- Michel A. Kervaire, Les nœuds de dimensions supérieures, Bull. Soc. Math. France 93 (1965), 225–271 (French). MR 189052 —, Knot cobordism in codimension two, Manifolds (Amsterdam, 1970), Lecture Notes in Math., vol. 190, Springer-Verlag, Berlin and New York.
- 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, Polynomial invariants of knots of codimension two, Ann. of Math. (2) 84 (1966), 537–554. MR 200922, DOI 10.2307/1970459
- 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
- H. F. Trotter, Homology of group systems with applications to knot theory, Ann. of Math. (2) 76 (1962), 464–498. MR 143201, DOI 10.2307/1970369
- H. F. Trotter, On $S$-equivalence of Seifert matrices, Invent. Math. 20 (1973), 173–207. MR 645546, DOI 10.1007/BF01394094
- Neal W. Stoltzfus, Unraveling the integral knot concordance group, Mem. Amer. Math. Soc. 12 (1977), no. 192, iv+91. MR 467764, DOI 10.1090/memo/0192
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 281 (1984), 529-570
- MSC: Primary 57Q45; Secondary 55P15
- DOI: https://doi.org/10.1090/S0002-9947-1984-0722762-1
- MathSciNet review: 722762