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Twisting formulae of the Jones polynomial

Published online by Cambridge University Press:  24 October 2008

Yoshiyuki Yokota
Yoshiyuki Yokota
Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, Ohkubo, Shinjuku, Tokyo, 169, Japan
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Extract

Let be an oriented knot in S3 and a solid torus endowed with a preferred framing which contains in its interior. By ρ and λ we denote the wrapping and winding numbers of in respectively. That is, they are the geometric and algebraic intersection numbers of and a meridian disk of . For an integer μ, let τμ be an orientation-preserving homeomorphism of satisfying τμ(m) = m and τμ(l) = l + μm in H1(∂), where (m, l) is a meridian-longitude pair of . We call τμ(), denoted by μ, the knot obtained from by μ-twisting along .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 473 - 482
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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