On Coxeter mapping classes and fibered alternating links

Hironaka, Eriko; Liechti, Nicola Livio (2016). On Coxeter mapping classes and fibered alternating links. Michigan mathematical journal, 65(4), pp. 799-812. University of Michigan Press 10.1307/mmj/1480734020

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Alternating-sign Hopf plumbing along a tree yields fibered alternating links whose homological monodromy is, up to a sign, conjugate to some alternating-sign Coxeter transformation. Exploiting this tie, we obtain results about the location of zeros of the Alexander polynomial of the fibered link complement implying a strong case of Hoste’s conjecture, the trapezoidal conjecture, bi-orderability of the link group, and a sharp lower bound for the homological dilatation of the monodromy of the fibration. The results extend to more general hyperbolic fibered 3-manifolds associated to alternating-sign Coxeter graphs.

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