Braids and the jones polynomial

John Franks, R. F. Williams

Research output: Contribution to journalArticlepeer-review

123 Scopus citations


An important new invariant of knots and links is the Jones polynomial, and the subsequent generalized Jones polynomial or two-variable polynomial. We prove inequalities relating the number of strands and the crossing number of a braid with the exponents of the variables in the generalized Jones polynomial which is associated to the link formed from the braid by connecting the bottom ends to the top ends. We also relate an exponent in the polynomial to the number of components of this link.

Original languageEnglish (US)
Pages (from-to)97-108
Number of pages12
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - Sep 1987

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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