Open Access
January 2016 Signature, positive Hopf plumbing and the Coxeter transformation
Livio Liechti
Osaka J. Math. 53(1): 251-267 (January 2016).


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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Livio Liechti. "Signature, positive Hopf plumbing and the Coxeter transformation." Osaka J. Math. 53 (1) 251 - 267, January 2016.


Published: January 2016
First available in Project Euclid: 19 February 2016

zbMATH: 1347.57016
MathSciNet: MR3466832

Primary: 57M27
Secondary: 20F55

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics

Vol.53 • No. 1 • January 2016
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