Zeros of the Jones Polynomial are Dense in the Complex Plane
Copyright policy )Zeros of the Jones Polynomial are Dense in the Complex Plane
In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of 'ring of tangles' links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weiss's theorem and Sokal's lemma, we prove that zeros of Jones polynomials of (pretzel) links are dense in the whole complex plane.
- Nanyang Technological University Singapore
- Xiamen University China (People's Republic of)
- National Institute of Education Singapore
Tutte polynomial of a signed graph, Invariants of knots and \(3\)-manifolds, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, FAMILIES, GRAPHS, LINKS, Planar graphs; geometric and topological aspects of graph theory, Signed and weighted graphs, KNOTS, Graph polynomials, Knots and links in the \(3\)-sphere, Relations of low-dimensional topology with graph theory
Tutte polynomial of a signed graph, Invariants of knots and \(3\)-manifolds, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, FAMILIES, GRAPHS, LINKS, Planar graphs; geometric and topological aspects of graph theory, Signed and weighted graphs, KNOTS, Graph polynomials, Knots and links in the \(3\)-sphere, Relations of low-dimensional topology with graph theory
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