Morse theory for plane algebraic curves

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.

31 pages, 9 figures. Many improvements since the last version. Proof of Proposition 2.9 completely rewritten, altough still long and technical

References in corpus (4)

• Knot Floer homology and the four-ball genus
• A concordance invariant from the Floer homology of +/- 1 surgeries
• Spectrum of plane curves via knot theory
• Deformations of singularities of plane curves. Topological approach

Cited by in corpus (3)

• Spectrum of plane curves via knot theory
• Cross-sections of unknotted ribbon disks and algebraic curves
• Realization of intermediate links of line arrangements