Twisting formulae of the Jones polynomial
Published online by Cambridge University Press: 24 October 2008
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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