Chord Diagrams and Coxeter Links

This paper presents a construction of fibered links $(K,\mathrm{\Sigma })$ out of chord diagrams $\text{sL}$. Let $\mathrm{\Gamma }$ be the incidence graph of $\text{sL}$. Under certain conditions on $\text{sL}$ the symmetrized Seifert matrix of $(K,\mathrm{\Sigma })$ equals the bilinear form of the simply-laced Coxeter system $(W,S)$ associated to $\mathrm{\Gamma }$; and the monodromy of $(K,\mathrm{\Sigma })$ equals minus the Coxeter element of $(W,S)$. Lehmer’s problem is solved for the monodromy of these Coxeter links.