On the strongly pseudoconcave boundary of a compact complex surface

Abstract

In this paper, we establish the method of holomorphic handle attaching to the strongly pseudoconcave boundary of a complex surface. We use this for proving the following statements: (1) every closed connected oriented contact 3 3 -manifold can be filled as the strongly pseudoconcave boundary of a compact complex surface; (2) any two non-empty closed connected oriented contact 3 3 -manifolds are complex cobordant. Moreover, we show that such a complex surface (or complex cobordism) can be taken Kähler.