The homological content of the Jones representations at $q = -1$

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  • Jens Kristian Egsgaard, Denmark
  • Søren Fuglede Jørgensen, Department of Mathematics, Uppsala University
We generalize a discovery of Kasahara and show that the Jones representations of braid groups, when evaluated at $q = -1$, are related to the action on homology of a branched double cover of the underlying punctured disk. As an application, we prove for a large family of pseudo-Anosov mapping classes a conjecture put forward by Andersen, Masbaum, and Ueno by extending their original argument for the sphere with four marked points to our more general case.
Original languageEnglish
PublisherarXiv.org
Number of pages20
Publication statusPublished - 25 Feb 2014

    Research areas

  • math.GT, math.QA

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