Chord Diagrams and Coxeter Links

Abstract

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