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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Liechti, Livio Nicola

Subjects:

500 Science > 510 Mathematics

ISSN:

0030-6126

Publisher:

Osaka University and Osaka City University, Departments of Mathematics

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

08 Jun 2016 10:44

Last Modified:

19 Jun 2016 19:50

ArXiv ID:

1401.5336v3

BORIS DOI:

10.7892/boris.80898

URI:

https://boris.unibe.ch/id/eprint/80898

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