Abstract
The Jones polynomial invariant of oriented links has already been expressed by means of a so-called skein formula in Proposition 3.7. and a similar, but different, formula was given for the Conway polynomial in Theorem 8.6. It will now be shown that those are two instances of a more general polynomial invariant in two indeterminates, sometimes called the HOMFLY polynomial ([31], [90], [106]). This is one of two two-variable generalisations of the Jones invariant. The other is the Kauffman polynomial invariant ([60], [58], [16], [45]). The main aim of this chapter is to show that these two invariants exist—that is, that they are indeed well defined. These proofs of existence are harder than the one given for the Jones polynomial in Chapter 3.
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© 1997 Springer Science+Business Media New York
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Lickorish, W.B.R. (1997). Generalisations of the Jones Polynomial. In: An Introduction to Knot Theory. Graduate Texts in Mathematics, vol 175. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0691-0_15
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DOI: https://doi.org/10.1007/978-1-4612-0691-0_15
Publisher Name: Springer, New York, NY
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