Real tight contact structures on lens spaces and surface singularities

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ONARAN S., Ozturk F.

Journal of Topology and Analysis, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s1793525323500139
  • Dergi Adı: Journal of Topology and Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: equivariant contact surgery, real open book decompositions, Real tight
  • Hacettepe Üniversitesi Adresli: Evet

Özet

We give a partial classification for the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on S3 and real lens spaces L(p,±1). We prove that there is a unique real tight S3 and P3. We show that there is at most one real tight L(p,±1) with respect to one of its two possible real structures. With respect to the other we give lower and upper bounds for the count. To establish lower bounds we explicitly construct real tight manifolds through equivariant contact surgery, real open book decompositions and isolated real algebraic surface singularities. As a by-product we observe the existence of an invariant torus in an L(p,p - 1) which cannot be made convex equivariantly.