paper

Cutting arcs for torus links and trees

arXiv:1409.0644 · doi:10.24033/bsmf.2747

Abstract

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., $A_{n}$ , $D_{n}$ , $E_{6}$ , $E_{7}$ and $E_{8}$ ) among all positive tree-like Hopf plumbings.

27 pages, 18 figures. Results have been extended to cover all Coxeter-Dynkin trees in the new version