Morse theory for plane algebraic curves
Geometric Topology
2014-02-26 v2 Algebraic Geometry
Abstract
We use Morse theoretical arguments to study algebraic curves in C^2. We take an algebraic curve C in C^2 and intersect it with a family of spheres with fixed origin and varying radii. We explain in detail how does the resulting link change when we cross a singular point of C. Applying link invariants as Murasugi's signature and Levine--Tristram signatures we obtain some informations about possible singularities of a curve C in terms of its topology.
Cite
@article{arxiv.1101.1870,
title = {Morse theory for plane algebraic curves},
author = {Maciej Borodzik},
journal= {arXiv preprint arXiv:1101.1870},
year = {2014}
}
Comments
31 pages, 9 figures. Many improvements since the last version. Proof of Proposition 2.9 completely rewritten, altough still long and technical