Shadows, ribbon surfaces, and quantum invariants

  • Alessio Carrega

    Università di Pisa, Italy
  • Bruno Martelli

    Università di Pisa, Italy

Abstract

Eisermann has shown that the Jones polynomial of a -component ribbon link is divided by the Jones polynomial of the trivial -component link. We improve this theorem by extending its range of application from links in to colored knotted trivalent graphs in , the connected sum of copies of .

We show in particular that if the Kauffman bracket of a knot in has a pole in of order , the ribbon genus of the knot is at least . We construct some families of knots in for which this lower bound is sharp and arbitrarily big. We prove these estimates using Turaev shadows.

Cite this article

Alessio Carrega, Bruno Martelli, Shadows, ribbon surfaces, and quantum invariants. Quantum Topol. 8 (2017), no. 2, pp. 249–294

DOI 10.4171/QT/90