English

Signature, positive Hopf plumbing and the Coxeter transformation

Geometric Topology 2020-03-27 v3

Abstract

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.

Keywords

Cite

@article{arxiv.1401.5336,
  title  = {Signature, positive Hopf plumbing and the Coxeter transformation},
  author = {Livio Liechti},
  journal= {arXiv preprint arXiv:1401.5336},
  year   = {2020}
}

Comments

16 pages, 5 figures, with appendix by Peter Feller and Livio Liechti