Every real 3-manifold is real contact
Journal of Symplectic Geometry, cilt.20, sa.6, ss.1313-1347, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 6
- Basım Tarihi: 2022
- Doi Numarası: 10.4310/jsg.2022.v20.n6.a3
- Dergi Adı: Journal of Symplectic Geometry
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.1313-1347
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Boğaziçi Üniversitesi Adresli: Evet
Özet
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact dis-tribution that is antisymmetric with respect to the real structure. We show that every real 3-manifold can be obtained via surgery along invariant knots starting from the standard real S3 and that this operation can be performed in the contact setting too. Using this result we prove that any real 3-manifold admits a real contact structure. As a corollary we show that any oriented over-twisted contact structure on an integer homology real 3-sphere can be isotoped to be real. Finally we give construction examples on S1 × S2 and lens spaces. For instance on every lens space there exists a unique real structure that acts on each Heegaard torus as hyperellipic involution. We show that any tight contact structure on any lens space is real with respect to that real structure.