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Computing ribbon obstructions for colored knots

Volume 253 / 2021

Patricia Cahn, Alexandra Kjuchukova Fundamenta Mathematicae 253 (2021), 155-173 MSC: Primary 57M12; Secondary 57K10, 57N70. DOI: 10.4064/fm767-7-2020 Published online: 26 November 2020

Abstract

Kjuchukova’s $\varXi _p$ invariant gives a ribbon obstruction for Fox $p$-colored knots. The invariant is derived from dihedral branched covers of 4-manifolds, and can be used to calculate the signatures of these covers when singularities on the branching sets are present. In this note, we give an algorithm for evaluating $\varXi _p$ from a colored knot diagram, and compute a couple of examples.

Authors

  • Patricia CahnSmith College
    Clark Science Center
    44 College Lane
    Northampton, MA 01063, U.S.A.
    e-mail
  • Alexandra KjuchukovaMax Planck Institute for Mathematics
    Vivatsgasse 7
    53111 Bonn, Germany
    e-mail

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