Chord diagrams and Coxeter links

Eriko Hironaka

This paper presents a construction of fibered links (K,\Sigma) out of chord diagrams \mathcal L. Let Gamma be the incidence graph of \mathcal L. Under certain conditions on \mathcal L 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.