Real algebraic overtwisted contact structures on 3-spheres
Algebraic and Geometric Topology, cilt.25, sa.3, ss.1377-1409, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 25 Sayı: 3
- Basım Tarihi: 2025
- Doi Numarası: 10.2140/agt.2025.25.1377
- Dergi Adı: Algebraic and Geometric Topology
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.1377-1409
- Anahtar Kelimeler: overtwisted contact structure, real algebraic link
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Boğaziçi Üniversitesi Adresli: Evet
Özet
A real algebraic link in the 3-sphere is defined as the zero locus in the 3-sphere of a real algebraic function from R4 to R2 with an isolated singularity at the origin. A real algebraic open book decomposition on the 3-sphere is by definition the Milnor fibration of such a real algebraic function. We prove that every overtwisted contact structure on the 3-sphere with positive three-dimensional invariant d3 (apart from 13 exceptions) are real algebraic via functions of the form (Formula Presented) with f; g complex algebraic and with the pages of the associated open books planar.