Signature, positive Hopf plumbing and the Coxeter transformation

Liechti, Livio Nicola (2016). Signature, positive Hopf plumbing and the Coxeter transformation. Osaka Journal of Mathematics, 53(1), pp. 251-267. Osaka University and Osaka City University, Departments of Mathematics

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By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.

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