Proof of the Rokhlin's Conjecture on Arnold's surfaces
| dc.creator | Nicou, F. | |
| dc.date | 2000-03-28 | |
| dc.date | 2002-11-22 | |
| dc.date.accessioned | 2026-07-25T22:42:35Z | |
| dc.description | 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. | |
| dc.description | 151 pages, latex file, section 2 of chapter 2 added to the previous version | |
| dc.identifier | https://arxiv.org/abs/math/0003182 | |
| dc.identifier | http://arxiv.org/abs/math/0003182 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/91729 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Proof of the Rokhlin's Conjecture on Arnold's surfaces | |
| dc.type | text |