publication . Preprint . Article . 2014

Shadows, ribbon surfaces, and quantum invariants

Alessio Carrega; Bruno Martelli;
Open Access English
  • Published: 23 Apr 2014
Eisermann has shown that the Jones polynomial of a $n$-component ribbon link $L\subset S^3$ is divided by the Jones polynomial of the trivial $n$-component link. We improve this theorem by extending its range of application from links in $S^3$ to colored knotted trivalent graphs in $\#_g(S^2\times S^1)$, the connected sum of $g\geqslant 0$ copies of $S^2\times S^1$. We show in particular that if the Kauffman bracket of a knot in $\#_g(S^2\times S^1)$ has a pole in $q=i$ of order $n$, the ribbon genus of the knot is at least $\frac {n+1}2$. We construct some families of knots in $\#_g(S^2\times S^1)$ for which this lower bound is sharp and arbitrarily big. We pro...
arXiv: Mathematics::Geometric TopologyMathematics::Quantum Algebra
free text keywords: Mathematics - Geometric Topology, Pure mathematics, Ribbon, Invariant (mathematics), Quantum, Algebra, Mathematics
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publication . Preprint . Article . 2014

Shadows, ribbon surfaces, and quantum invariants

Alessio Carrega; Bruno Martelli;