Nuclei and exotic 4-manifolds

Details Nuclei and exotic 4-manifolds Nuclei and exotic 4-manifolds

2011-11-02

arxiv.org/abs/1111.0620v2

Mathematics

Geometric Topology

36 pages, 17 figures, minor improvements and corrections

Scientific paper

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.

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