Proof of the Rokhlin's Conjecture on Arnold's surfaces

Details Proof of the Rokhlin's Conjecture on Arnold's surfaces Proof of the Rokhlin's Conjecture on Arnold's surfaces

2000-03-28

arxiv.org/abs/math/0003182v3

Mathematics

Algebraic Geometry

151 pages, latex file, section 2 of chapter 2 added to the previous version

Scientific paper

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.

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