×

zbMATH — the first resource for mathematics

Periodicity of branched cyclic covers. (English) Zbl 0296.55001

MSC:
57M10 Covering spaces and low-dimensional topology
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
14B05 Singularities in algebraic geometry
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Brieskorn, E.: Beispiele zur Differenzialtopologie von Singularitäten. Inventiones Math.2, 1-14 (1966) · Zbl 0145.17804 · doi:10.1007/BF01403388
[2] Durfee, A.: Diffeomorphism classification of isolated hypersurface singularities, Thesis, Cornell (1971). (Revised version to appear, under the title ?Bilinear and quadratic forms on torsion modules?, in Advances in math.)
[3] Durfee, A.: Fibered knots and algebraic singularities. Topology13, 47-59 (1974) · Zbl 0275.57007 · doi:10.1016/0040-9383(74)90037-8
[4] Erle, D.: Quadratische Formen als Invarianten von Einbettungen der Codimension 2. Topology8, 99-114 (1969) · Zbl 0157.30901 · doi:10.1016/0040-9383(69)90002-0
[5] Fox, R.: Covering spaces with singularities. In: Algebraic Geometry and Topology, A Symposium in Honor of S. Lefschetz. Princeton University Press pp. 243-257, 1957 · Zbl 0079.16505
[6] Fox, R.: The homology characters of the cyclic coverings of the knots of genus one. Ann. of Math. (2)71, 187-196 (1960) · Zbl 0122.41801 · doi:10.2307/1969886
[7] Gabrielov, A.: Intersection matrices of certain singularities. Funk. anal. i jewo pril7, 18-32 (1973) (in Russian)
[8] Gordon, C.: Knots whose branched cyclic coverings have periodic homology. Trans. Amer. Math. Soc.168, 357-370 (1972) · Zbl 0238.55001 · doi:10.1090/S0002-9947-1972-0295327-8
[9] Kauffman, L.: Cyclic branched covers, 0(n)-actions and hypersurface singularities. Thesis, Princeton (1972) · Zbl 0249.57024
[10] Kauffman, L.: Link manifolds and periodicity, Bull. Amer. Math. Soc.79, 570-573 (1973) · Zbl 0258.57019 · doi:10.1090/S0002-9904-1973-13207-0
[11] Kauffman, L.: Branched coverings, open books, and knot periodicity. Topology13, 143-160 (1974) · Zbl 0283.57011 · doi:10.1016/0040-9383(74)90005-6
[12] Kaufmann, L.: Products of knots. Bull. Amer. Math. Soc.80, 1104-1107 (1974) · Zbl 0299.57008 · doi:10.1090/S0002-9904-1974-13629-3
[13] Kaufman, L., Taylor, L.: Signature of links (to appear)
[14] Levine, J.: Polynomial invariants of knots of codimension two. Ann. of Math.84, 537-554 (1966) · Zbl 0196.55905 · doi:10.2307/1970459
[15] Levine, J.: Knot cobordism groups in codimension two. Comm. Math. Helv.44, 229-244 (1969) · Zbl 0176.22101 · doi:10.1007/BF02564525
[16] Milnor, J.: Singular points of complex hypersurfaces. Princeton University Press 1968 · Zbl 0184.48405
[17] Neumann, W.: Cyclic suspension of knots and periodicity of signature for singularities. Bull. Amer. Math. Soc.80, 977-981 (1974) · Zbl 0292.57013 · doi:10.1090/S0002-9904-1974-13605-0
[18] Sakamoto, K.: The Seifert matrix of Milnor fiberings defined by holomorphic functions. J. Math. Soc. Japan26, 714-721 (1974) · Zbl 0286.32010 · doi:10.2969/jmsj/02640714
[19] Sebastiani, M., Thom, R.: Un résultat sur la monodromie. Inventiones Math.13, 90-96 (1971) · Zbl 0233.32025 · doi:10.1007/BF01390095
[20] Seifert, H.: Die Verschlingungsinvarienten der zyklischen Knotenüberlagerungen. Hamb. Abh.11, 84-101 (1936) · Zbl 0011.17802 · doi:10.1007/BF02940716
[21] Seifert, H., Threlfall, W.: Lehrbuch der Topologie. Chelsea 1934 · Zbl 0009.08601
[22] Tristram, A.: Some cobordism invariants for links. Proc. Camb. Phil. Soc.66, 251-264 (1969) · Zbl 0191.54703 · doi:10.1017/S0305004100044947
[23] Wall, C. T. C.: Classification of (n-1)-connected 2n-manifolds. Ann. of Math.75, 163-189 (1962) · Zbl 0218.57022 · doi:10.2307/1970425
[24] Wall, C. T. C.: Classification problems in differential topology. VI. Classification of (s-1)-connected (2s+1)-manifolds. Topology6, 273-296 (1967) · Zbl 0173.26102 · doi:10.1016/0040-9383(67)90020-1
[25] Woods, J.: Periodicity for the homology of finite cyclic coverings and the monodromy map of algebraic links. Thesis. Florida State University 1973
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.