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arXiv · 2012.03018

On the strongly pseudoconcave boundary of a compact complex surface

Naohiko Kasuya·Daniele Zuddas
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Abstract

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-manifold can be filled as the strongly pseudoconcave boundary of a compact complex surface; (2) any two closed connected oriented contact 3-manifolds are complex cobordant. Moreover, we show that such complex surface (or complex cobordism) can be taken K\"ahler.

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Naohiko Kasuya, Daniele Zuddas. 2020-12-05. On the strongly pseudoconcave boundary of a compact complex surface. https://arxiv.org/abs/2012.03018

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