Nuclei and exotic 4-manifolds

Abstract

We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants. We prove that a large class of closed 3-manifolds (including disjoint unions of Stein fillable 3-manifolds) bound compact connected oriented 4-manifolds which admit infinitely many smooth structures. To detect smooth structures, we introduce a relative genus function. As a side result, we show that log transform and knot surgery of 4-manifolds do not admit any Stein structure, under a mild condition. Applying these results together with corks, we construct arbitrary many compact Stein 4-manifolds and infinitely many non-Stein 4-manifolds which are all homeomorphic but mutually non-diffeomorphic.

36 pages, 17 figures, minor improvements and corrections

References in corpus (4)

• Corks, Plugs and exotic structures
• Surgery on Nullhomologous Tori
• Knotted surfaces in 4-manifolds
• Cork twisting exotic Stein 4-manifolds

Cited by in corpus (7)

• On the geometrization of matter by exotic smoothness
• Smooth embeddings with Stein surface images
• Minimal genera of open 4-manifolds
• Infinitely many small exotic Stein fillings
• Partial twists and exotic Stein fillings
• Corks with large shadow-complexity and exotic 4-manifolds
• Nonexistence of twists and surgeries generating exotic 4-manifolds