Maximally writhed real algebraic links

• 成果类型: Article
• 署名作者: Mikhalkin, Grigory; Orevkov, Stepan
• 署名单位: University of Geneva; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0844-7
• 发表日期: 2019
• 页码: 125-152
• 关键词: enumeration

摘要

Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots and links in RP3 which is not a topological isotopy invariant. In this paper we study real algebraic links of degree d with the maximal value of this invariant. We show that these links admit entirely topological description. In particular, these links are characterized by the property that any of their planar diagram has at least (d-1)(d-2)/2-g-1 crossing points where g is the genus of the complexification. Also we show that these links are characterized by the property that any generic plane intersects them in at least d-2 real points. In addition we give a complete topological classification of these links.