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 Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 4, Pages 794–828 (Mi izv1868)

Duality in an infinite cyclic covering and even-dimensional knots

M. Sh. Farber

Abstract: Pairings are constructed defined on the torsion subgroups of the integral homology groups of the infinite cyclic covering of a compact manifold with values in the factor group of the rationals modulo the integers. This gives invariants of even-dimensional knots, with the help of which three problems of R. H. Fox about two-dimensional knots in four-dimensional space are solved.
Bibliography: 25 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:4, 749–781

Bibliographic databases:

UDC: 513.83
MSC: 57C45

Citation: M. Sh. Farber, “Duality in an infinite cyclic covering and even-dimensional knots”, Izv. Akad. Nauk SSSR Ser. Mat., 41:4 (1977), 794–828; Math. USSR-Izv., 11:4 (1977), 749–781

Citation in format AMSBIB
\Bibitem{Far77} \by M.~Sh.~Farber \paper Duality in an infinite cyclic covering and even-dimensional knots \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1977 \vol 41 \issue 4 \pages 794--828 \mathnet{http://mi.mathnet.ru/izv1868} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=515677} \zmath{https://zbmath.org/?q=an:0366.55003} \transl \jour Math. USSR-Izv. \yr 1977 \vol 11 \issue 4 \pages 749--781 \crossref{https://doi.org/10.1070/IM1977v011n04ABEH001744} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. Sh. Farber, “Classification of certain higher-dimensional knots of codimension two”, Russian Math. Surveys, 35:3 (1980), 123–130
2. Jonathan A. Hillman, “Finite knot modules and the factorization of certain simple knots”, Math Ann, 257:2 (1981), 261
3. M. Sh. Farber, “Classification of stable fibered knots”, Math. USSR-Sb., 43:2 (1982), 199–234
4. M. Sh. Farber, “The classification of simple knots”, Russian Math. Surveys, 38:5 (1983), 63–117
5. Jonathan A. Hillman, “Abelian normal subgroups of two-knot groups”, Comment Math Helv, 61:1 (1986), 122
6. EIJI OGASA, “RIBBON-MOVES OF 2-KNOTS: THE TORSION LINKING PAIRING AND THE $\tilde{\eta}$-INVARIANTS OF 2-KNOTS”, J. Knot Theor. Rev, 16:5 (2007), 523
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