Jones polynomial invariants

Andrew Fish, Ebru Keyman

Research output: Contribution to journalArticle

Abstract

The Jones polynomial is a well-defined invariant of virtual links. We observe the effect of a generalised mutation M of a link on the Jones polynomial. Using this, we describe a method for obtaining invariants of links which are also invariant under M . The Jones polynomial of welded links is not well-defined in Z[q 1/4 , q −1/4 ]. Taking M = Fo allows us to pass to a quotient of Z[q 1/4 , q −1/4 ] in which the Jones polynomial is well-defined. We get the same result for M = Fu , so in fact, the Jones polynomial in this ring defines a fused isotopy invariant. We show it is non-trivial and compute it for links with one or two components.
Original languageEnglish
Pages (from-to)339-350
Number of pages12
JournalJournal of Knot Theory and Its Ramifications
Volume15
Issue number3
DOIs
Publication statusPublished - 1 Mar 2006

Bibliographical note

© 2006 World Scientific Publishing Company

Keywords

  • Virtual links
  • Welded links
  • Jones polynomial

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