Morse theory for plane algebraic curves

Maciej Borodzik

doi:10.1112/jtopol/jts006

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arXiv · 1101.1870

Morse theory for plane algebraic curves

Maciej Borodzik

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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.

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Maciej Borodzik. 2011-05-24. Morse theory for plane algebraic curves. https://doi.org/10.1112/jtopol%2Fjts006

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