Abstract
This chapter contains some of the most impressive applications of the Jones polynomial. They give solutions to two problems encountered by P. G. Tait in the nineteenth century. It is shown that an alternating knot diagram, when “reduced” in a rather elementary way, has the minimal number of crossings and that its writhe is an invariant of the knot. The crossing number of some other types of knot is also determined.
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© 1997 Springer Science+Business Media New York
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Lickorish, W.B.R. (1997). The Jones Polynomial of an Alternating Link. 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_5
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DOI: https://doi.org/10.1007/978-1-4612-0691-0_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6869-7
Online ISBN: 978-1-4612-0691-0
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