Inventiones mathematicae

, Volume 20, Issue 3, pp 173–207 | Cite as

OnS-equivalence of Seifert matrices

  • H. F. Trotter


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Crowell, R.H.: The groupG′/G″ of a knot groupG. Duke Math. J.30, 349–354 (1963).Google Scholar
  2. 2.
    Crowell, R.H., Fox, R.H.: Introduction to Knot Theory. New York: Blaisdell 1963.Google Scholar
  3. 3.
    Erle, D.: Quadratische Formen als Invarianten von Einbettungen der Kodimension 2. Topology8, 99–114 (1969).Google Scholar
  4. 4.
    Fox, R.H.: The homology characters of the cyclic coverings of the knots of genus one. Ann. Math.71, 187–196 (1960).Google Scholar
  5. 5.
    Fox, R.H., Smythe, N.: An ideal class invariant of knots. Proc. Amer. Math. Soc.15, 707–709 (1964).Google Scholar
  6. 6.
    Levine, J.: An algebraic classification of some knots of codimension two. Comm. Math. Helv.45, 185–198 (1970).Google Scholar
  7. 7.
    Levine, J.: Polynomial invariants of knots of codimension two. Ann. Math.84, 537–554 (1966).Google Scholar
  8. 8.
    Levine, J.: Finite procedures in knot theory. (Mimeographed.) Brandeis University, 1972.Google Scholar
  9. 9.
    Milnor, J.: Infinite cyclic coverings. In: Conference on the Topology of Manifolds. Ed. J. G. Hocking. Boston: Prindle, Weber and Schmidt 1968.Google Scholar
  10. 10.
    Milnor, J.: On isometries of inner product spaces. Inventiones math.8, 83–97 (1969).Google Scholar
  11. 11.
    Murasugi, K.: On a certain numerical invariant of link types. Trans. Amer. Math. Soc.117, 387–422 (1965).Google Scholar
  12. 12.
    O'Meara, O.T.: Introduction to Quadratic Forms. New York: Academic Press 1963.Google Scholar
  13. 13.
    Rice, P.M.: Equivalence of Alexander Matrices. Math. Ann.193, 65–75 (1971).Google Scholar
  14. 14.
    Seifert, H.: Über das Geschlecht von Knoten. Math. Ann.110, 571–592 (1934).Google Scholar
  15. 15.
    Seifert, H.: Die Verschlingungsinvarianten der zyklischen Knotenüberlagerungen. Abh. Math. Sem. Hamburg Univ.11, 84–101 (1936).Google Scholar
  16. 16.
    Trotter, H.F.: Homology of group systems with applications to knot theory. Ann. Math.76, 464–498 (1962).Google Scholar
  17. 17.
    Trotter, H.F.: On the norms of units in quadratic fields. Proc. Amer. Math. Soc.22, 198–201 (1969).Google Scholar
  18. 18.
    Trotter, H.F.: On the algebraic classification of Seifert Matrices. Proceedings of the Georgia Topology Conference 1970, 92–103, University of Georgia, Athens, 1970 (mimeographed).Google Scholar
  19. 19.
    Dickson, L.E.: Introduction to the Theory of Numbers. Chicago: University of Chicago Press 1929.Google Scholar
  20. 20.
    Kearton, C.: Classification of simple knots by Blanchfield duality. Bull. Amer. Math. Soc. (to appear).Google Scholar
  21. 21.
    Blanchfield, R.C.: Intersection theory of manifolds with operators with applications to knot theory. Ann. Math.65, 340–356 (1957).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • H. F. Trotter
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations