Existence of almost complex structure of 4-manifold

Abstract

M이 컴팩트이고 유향인 리만 4차원 다양체일 때, almost 복소구조를 갖기 위한 장애다발(obstruction bundle)을 구성하고 M의 almost 복소구조가 M의 방향에 따라 의존함을 CP²의 예를 통해 보인다. ; Let M be a compact, oriented, Riemannian 4-manifold. Let TM be the tangent bundle of M and let ε associated SO(4) - principal bundle on M. We would like to introduce an associated bundle ε Which haS fiber SO(4) /SO(2)×SO(2)( S²× S²). We will show that the bundle is the obstruction bundle for the existence of almost complex structure on M and that the existence of almost complex structure on M depends on the orientations of M.