Morse theory for plane algebraic curves

Details Morse theory for plane algebraic curves Morse theory for plane algebraic curves

2011-01-10

arxiv.org/abs/1101.1870v2

Mathematics

Geometric Topology

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

Scientific paper

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.

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