Plane curve singularities via divides
Geometric Topology
2025-03-14 v1
Abstract
Generic relative immersions of compact one-manifolds in the closed unit disk, i.e. divides, provide a powerful combinatorial framework, and allow a topological construction of fibered classical links, for which the monodromy diffeomorphism is explicitly given as a product of Dehn twists. Complex isolated plane curve singularities provide a classical fibered link, the Milnor fibration, with its Milnor monodromy, monodromy group, and vanishing cycles. This surveys puts together much of the work done on divides and their role in the topology of isolated plane curve singularities.
Keywords
Cite
@article{arxiv.2503.10424,
title = {Plane curve singularities via divides},
author = {Norbert A'Campo and Pablo Portilla Cuadrado},
journal= {arXiv preprint arXiv:2503.10424},
year = {2025}
}
Comments
45 figures, 72 pages, longer abstract inside. arXiv admin note: text overlap with arXiv:math/0006124, arXiv:math/0301006, arXiv:math/9803081