Contact 5-manifolds and smooth structures on Stein 4-manifolds

Kouichi Yasui

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arXiv · 1604.03460

Contact 5-manifolds and smooth structures on Stein 4-manifolds

Kouichi Yasui

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Abstract

We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic Stein 4-manifolds. The proofs rely on the adjunction inequality. We remark that there are various examples of infinitely many pairwise exotic Stein 4-manifolds whose smooth structures can be distinguished by these results.

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Kouichi Yasui. 2016-04-12. Contact 5-manifolds and smooth structures on Stein 4-manifolds. https://arxiv.org/abs/1604.03460

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