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Signatures of Covering Links

Published online by Cambridge University Press:  20 November 2018

C. Mca. Gordon ,
R. A. Litherland  and
K. Murasugi
C. Mca. Gordon
Affiliation:
University of Texas, at Austin, Austin, Texas
R. A. Litherland
Affiliation:
University of Cambridge, Cambridge, England
K. Murasugi
Affiliation:
University of Toronto, Toronto, Ontario
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A (tame) knot kn in S3 is said to have period n if there exists a homeomorphism ϕ: S3 → S3, necessarily orientationpreserving, such that

  • (i) the fixed point set of ϕ is a circle disjoint from kn

  • (ii) ϕ(kn) = kn;

  • (iii) ϕ has order n.

Several necessary conditions for a knot to have period n have already been established in the literature; see [3] [11] [14] [18]. Here we establish the following further condition, involving the signature σ(kn) of (kn).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 2 , 01 April 1981 , pp. 381 - 394
Copyright
Copyright © Canadian Mathematical Society 1981

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