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Hermitian character and the first problem for R. H. Fox for links

Published online by Cambridge University Press:  24 October 2008

Adrian Pizer
Adrian Pizer
Affiliation:
Department of Mathematics, Osaka City University, Japan
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Extract

The fundamental group G of a μ-component link has the properties:

(1) G is finitely presented, with deficiency 1;

(2) G/G′ is free abelian on μ distinguished generators, say {t1 …, tμ}.

Let ψ: G → G/G′ → 〈t〉 be the composition of the canonical projection G → G/G′ and the epimorphism defined by . Then the Z〈t〉-module M = Ker ψ/(Ker ψ)′ (the so-called module of the link) has a square (say n × n) relation matrix N. We write [N] for the Z〈t〉-equivalence class of N (Fox [3], p. 199) and N′̅ for the conjugate transpose of N.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 77 - 86
Copyright
Copyright © Cambridge Philosophical Society 1987

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