Hostname: page-component-857557d7f7-ktsnh Total loading time: 0 Render date: 2025-11-20T17:24:22.043Z Has data issue: false hasContentIssue false
  • English
  • Français

Cancellation of hyperbolic ε-hermitian forms and of simple knots

Published online by Cambridge University Press:  24 October 2008

Eva Bayer-Fluckiger
Eva Bayer-Fluckiger
Affiliation:
Section de Mathématiques, Université de Genève, Switzerland
Get access Rights & Permissions [Opens in a new window]

Extract

An n-knot will be a smooth, oriented submanifold Kn ⊂ Sn+2 such that Kn is homeomorphic to Sn. Given two knots and , we define their connected sum as in [13], p. 39. The cancellation problem for n-knots is the following.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 111 - 115
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Bak, A. and Scharlau, W.. Grothendieck and Witt groups of orders and finite groups. Invent. Math. 23 (1974), 207–240.CrossRefGoogle Scholar
[2]Bayer, E.. Definite hermitian forms and the cancellation of simple knots. Archiv der Math. 40 (1983), 182–185.CrossRefGoogle Scholar
[3]Bayer-Fluckiger, E.. Higher dimensional simple knots and minimal Seifert surfaces. Comment. Math. Helv. 58 (1983), 646–655.CrossRefGoogle Scholar
[4]McA, C.. Gordon. Some higher-dimensional knots with the same homotopy groups. Quart. J. Math. Oxford Ser. (2), 24 (1973), 411–422.Google Scholar
[5]McA, C.. Gordon. A note on spun knots. Proc. Amer. Math. Soc. 58 (1976), 361–362.Google Scholar
[6]Kearton, C.. Blanchfield duality and simple knots. Trans. Amer. Math. Soc. 202 (1975), 141–160.CrossRefGoogle Scholar
[7]Kearton, C.. Spinning, factorisation of knots, and cyclic group actions on spheres. Arch. Math. 40 (1983), 361–363.CrossRefGoogle Scholar
[8]Kervaire, M.. Les noeuds de dimensions supérieures. Bull. Soc. Math. France 93 (1965), 225–271.Google Scholar
[9]Kervaire, M. and Weber, C.. A survey of multidimensional knots. In Knot Theory Proceedings, Plans-sur-Bex, Lecture Notes in Math. vol. 685. Springer-Verlag. (1977).Google Scholar
[10]Levine, J.. An algebraic classification of some knots of codimension two. Comm. Math. Helv. 45 (1970), 185–198.CrossRefGoogle Scholar
[11]O'Meara, . Introduction to Quadratic Forms. Springer-Verlag (1973).CrossRefGoogle Scholar
[12]Parimala, R.. Cancellation of quadratic forms over principal ideal domains. J. Pure Appl. Algebra 24 (1982), 213–216.CrossRefGoogle Scholar
[13]Rolfsen, D.. Knots and Links, Mathematics Lecture Notes, Series 7. Publish or Perish (1976).Google Scholar
[14]Schubert, H.. Die eindeutige Zerlegbarkeit eines Knotens in Primknoten. Sitzungsber. Heidelb. Akad. Wiss. Math.-Natur. Kl. 1, 3 (1949), 57–104.Google Scholar
[15]Trotter, H.. On S-equivalence of Seifert matrices. Invent. Math. 20 (1970), 173–207.CrossRefGoogle Scholar
[16]Trotter, H.. Knot modules and Seifert matrices. In Knot Theory Proceedings, Plana-sur-Bex, Lecture Notes in Math. vol. 685. Springer-Verlag (1977).Google Scholar
[17]Wiegand, R.. Cancellation over commutative rings of dimension one and two. J. Algebra 88 (1984), 438–459.CrossRefGoogle Scholar