On the topology of fillings of contact 3-manifolds

Abstract

Definition 1.2 An almost-complex structure on an even-dimensional manifold X is a complex structure on its tangent bundle TX , or equivalently a bundle map J W TX ! TX with J iJ D idTX . The pair .X;J / is called an almost complex manifold. It is called a complex manifold if the almost complex structure is integrable, meaning that J is induced via multiplication by i in any holomorphic coordinate chart.