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

2016/04/12 by Kouichi Yasui, Yasui, Kouichi · 1 citation
Mathematics · #57R17 #57R55 #57R65 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1604.03460

openalex publication_date 2016/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Nonexistence of twists and surgeries generating exotic 4-manifolds

Related

• Exotic structures and adjunction inequality
• Contact 5-manifolds admitting open books with exotic pages
• Infinitely many small exotic Stein fillings
• Families of contact 3-manifolds with arbitrarily large Stein fillings
• Higher-dimensional contact manifolds with infinitely many Stein fillings