Proof of the Rokhlin's Conjecture on Arnold's surfaces
Algebraic Geometry
2007-05-23 v3
Abstract
In this paper we prove that Arnold Surfaces of all real algebraic curves of even degree with non-empty real part are standard (Rokhlin's Conjecture). There is an obvious connection with classification of Arnold Surfaces up to isotopy of S^4 and Hilbert's Sixteen Problem on the arrangements of connected real components of curves. First, we consider some M-curves, i.e curves of a prescribed degree having the greatest possible number of connected real components, and prove that Arnold surfaces of these curves are standard. Afterwards, we exhibit a procedure of modification "perestroika" of these M-curves which allows to prove the Rokhlin's Conjecture.
Cite
@article{arxiv.math/0003182,
title = {Proof of the Rokhlin's Conjecture on Arnold's surfaces},
author = {F. Nicou},
journal= {arXiv preprint arXiv:math/0003182},
year = {2007}
}
Comments
151 pages, latex file, section 2 of chapter 2 added to the previous version