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Annals of Global Analysis and Geometry

, Volume 15, Issue 4, pp 325–334 | Cite as

Almost Complex Structures Which Are Compatible with Kähler or Symplectic Structures

  • Frank Connolly
  • Lê Hông Vân
  • Kaoru Ono
Article

Abstract

In this note we prove that half of all homotopy classes of almost complex structures on M is not compatible with any symplectic structure for a certain class of oriented compact 4-manifolds M. In particular, half of all homotopy classes of almost complex structures on an oriented 4-manifold is not compatible to any Kähler structure.

almost complex structure Kähler structure Seiberg–Witten invariant symplectic structure 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Frank Connolly
    • 1
  • Lê Hông Vân
    • 2
  • Kaoru Ono
    • 3
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameU.S.A
  2. 2.Max-Planck-Institut für MathematikBonnGermany
  3. 3.Department of MathematicsOchanomizu UniversityTokyoJapan

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