Count of genus zero J-holomorphic curves in dimensions four and six

BEYAZ A.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.1949-1958, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2007-72
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1949-1958
  • Anahtar Kelimeler: Symplectic manifolds, J-holomorphic curves, symplectic deformation equivalence, TOPOLOGY
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

An application of Gromov-Witten invariants is that they distinguish the deformation types of symplectic structures on a smooth manifold. In this manuscript, it is proven that the use of Gromov-Witten invariants in the class of embedded J-holomorphic spheres is restricted. This restriction is in the sense that they cannot distinguish the deformation types of symplectic structures on X-1 x S-2 and X-2 x S-2 for two minimal, simply connected, symplectic 4-manifolds X-1 and X-2 with b(2)(+) (X-1) > 1 and b(2)(+) (X-2) > 1. The result employs the adjunction inequality for symplectic 4-manifolds which is derived from Seiberg-Witten theory.