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Almost Complex Structures Which Are Compatible with Kähler or Symplectic Structures |
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| Authors: | Frank Connolly Lê Hông Vân Kaoru Ono |
| Affiliation: | (1) Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, U.S.A;(2) Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, 53225 Bonn, Germany;(3) Department of Mathematics, Ochanomizu University, Otsuka, Tokyo, 112, Japan |
| 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. |
| Keywords: | almost complex structure Kä hler structure Seiberg– Witten invariant symplectic structure |
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