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Relations between Kauffman and Homfly satellite invariants

Published online by Cambridge University Press:  16 March 2010

H. R. MORTON
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL. e-mail: su14@liverpool.ac.uk
N. D. A. RYDER
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL. e-mail: su14@liverpool.ac.uk

Abstract

We extend a mod 2 relation between the Kauffman and Homfly polynomials, first observed by Rudolph in 1987, to the general Kauffman and Homfly satellite invariants.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

REFERENCES

[1]Beliakova, A. and Blanchet, C.Skein construction of idempotents in Birman–Murakami–Wenzl algebras. Math. Ann. 321 (2001), 347373.CrossRefGoogle Scholar
[2]Hadji, R. J. Homfly skein theory of reversed string satellites. PhD thesis, University of Liverpool (2003).Google Scholar
[3]Hadji, R. J. and Morton, H. R.A basis for the full Homfly skein of the annulus. Math. Proc. Camb. Phil. Soc. 141 (2006), 81100.CrossRefGoogle Scholar
[4]Morton, H. R.Integrality of Homfly 1-tangle invariants. Algebr. Geom. Topol. 7 (2007), 327338.CrossRefGoogle Scholar
[5]Rudolph, L.A congruence between link polynomials. Math. Proc. Camb. Phil. Soc. 107 (1990), 319327.CrossRefGoogle Scholar
[6]Ryder, N. D. A. Skein based invariants and the Kauffman polynomial. PhD thesis, University of Liverpool (2008).Google Scholar
[7]Lu, B. and Zhong, J. K.The Kauffman polynomials of generalized Hopf links. J. Knot Theory Ramifications 11 (2002), 12911306.CrossRefGoogle Scholar