Geodesic
Classification of stable fibered knots
Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 199-234 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper a new invariant of fibered knots is studied, represented as a homotopy pairing in the sense of Spanier and Whitehead. With its help, first of all, a classification of stable fibered knots is given; second, it is shown that certain well-known invariants in knot theory define the type of a stable knot up to a finite number of possibilities; and third, a complete algebraic description of certain classes of knots is given. Figures: 3. Bibliography: 33 titles. 
@article{SM_1982_43_2_a3,
     author = {M. Sh. Farber},
     title = {Classification of stable fibered knots},
     journal = {Sbornik. Mathematics},
     pages = {199--234},
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     volume = {43},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_43_2_a3/}
}
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M. Sh. Farber. Classification of stable fibered knots. Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 199-234. http://geodesic.mathdoc.fr/item/SM_1982_43_2_a3/

[1] Browder W., “Diffeomorphisms of 1-connected manifolds”, Trans. Amer. Math. Soc., 128 (1967), 155–163 | DOI | MR | Zbl

[2] Bredon G. E., “Regular $O(n)$-manifolds, suspension of knots and knot periodicity”, Bull. Amer. Math. Soc., 79 (1973), 87–91 | DOI | MR | Zbl

[3] Burde G., “Knoten”, Jahrbuch Überlicke Math., 1978, 131–147 | MR | Zbl

[4] Dold A., “Polutochnye gomotopicheskie funktory”, Matematika, 14:1 (1970), 3–93 | MR | Zbl

[5] Durfee A., Lawson H., “Fibred knots and foliations of highly connected manifolds”, Invent. Math., 17 (1972), 203–215 | DOI | MR | Zbl

[6] Durfee A., “Fibred knots and algebraic singularities”, Topology, 13 (1974), 47–59 | DOI | MR | Zbl

[7] Eilenberg S., Maclane S., “On the groups $H(\pi,n)$. II. Methods of computations”, Ann. Math., 60:2 (1954), 49–139 | DOI | MR | Zbl

[8] Farber M. Sh., “Koeffitsienty zaschepleniya i dvumernye uzly”, DAN SSSR, 222:2 (1975), 299–301 | MR | Zbl

[9] Farber M. Sh., “Dvoistvennost v beskonechnom tsiklicheskom nakrytii i chetnomernye uzly”, Izv. AN SSSR, ser. matem., 41 (1977), 794–828 | MR | Zbl

[10] Farber M. Sh., “Klassifikatsiya nekotorykh uzlov korazmernosti dva”, DAN SSSR, 204:1 (1978), 32–35 | MR

[11] Farber M. Sh., “Klassifikatsiya nekotorykh mnogomernykh uzlov korazmernosti dva”, UMN, 35:3 (1980), 105–111 | MR | Zbl

[12] Farber M. Š., “Isotopy types of knots of codimension two”, Trans. Amer. Math. Soc., 261:1 (1980), 185–209 | DOI | MR

[13] Hausmann J.-Cl., Noeuds antisimples, Lecture Notes in Math., 685, 1978 | MR

[14] Khirsh M., Differentsialnaya topologiya, Mir, M., 1979 | MR | Zbl

[15] Kahn D. W., “The group of stable self-equivalences”, Topology, 11 (1972), 133–140 | DOI | MR | Zbl

[16] Kauffman L. H., Neumann W. D., “Products of knots, branched fibrations and sums of singlarities”, Topology, 16 (1977), 369–393 | DOI | MR | Zbl

[17] Kearton C., “Blanchfield duality and simple knots”, Trans. Amer. Math. Soc., 202 (1975), 141–160 | DOI | MR | Zbl

[18] Kearton C., “A classification of some even dimensional knots”, Topology, 15 (1976), 363–373 | DOI | MR | Zbl

[19] Kervaire M. A., “Les noeuds de dimensions superieures”, Bull. Soc Math. France, 93 (1965), 225–271 | MR | Zbl

[20] Kajima S., “A classification of some even dimensional fibred knots”, J. Fac Sci. Univ. Tokyo, 24 (1977), 671–683 | MR

[21] Kojima S., “Classification of simple knots by Levine pairings”, Comm. Math. Helv., 54 (1979), 356–367 | DOI | MR | Zbl

[22] Levine J., “An algebraic classification of some knots of codimension two”, Comm. Math. Helv., 45 (1970), 185–198 | DOI | MR | Zbl

[23] Levine J., Knot modules, Ann. Math. Studies, Princeton Univ. Press, 1975 | MR

[24] Levine J., “Knot nodules. I”, Trans. Amer. Math. Soc., 229 (1977), 1–50 | DOI | MR | Zbl

[25] Milnor Dzh., Osobye tochki kompleksnykh giperpoverkhnostei, Mir, M., 1971 | MR | Zbl

[26] Mosher R., Tangora M., Kogomologicheskie operatsii i ikh primeneniya v teorii gomotopii, Mir, M., 1970 | Zbl

[27] Novikov S. P., “O mnogoobraziyakh so svobodnoi abelevoi fundamentalnoi gruppoi i ikh primeneniyakh”, Izv. AN SSSR, ser. matem., 30 (1966), 207 | Zbl

[28] Schubert H., “Knoten mit zwei Brucken”, Math. Z., 1956, no. 65, 133–170 | DOI | MR | Zbl

[29] Spener E., Algebraicheskaya topologiya, 1971, Mir, M. | MR

[30] Spanier E., “Infinite symmetric products, function spaces and duality”, Ann. Math., 69 (1959), 142–198 | DOI | MR | Zbl

[31] Durfee A., “Foliations of odd-dimensional spheres”, Ann. Math., 96:2 (1972), 407–411 | DOI | MR | Zbl

[32] Trotter H., “On $S$-equivalence of Seifert matrices”, Invent. Math., 20 (1973), 173–207 | DOI | MR | Zbl

[33] Viro O. Ya., Lokalnoe zauzlivanie podmnogoobrazii, 90 (132) (1973), 173–183 | MR | Zbl