On 3-manifolds that are boundaries of exotic 4-manifolds

2019/01/23 by Etnyre, John B., Min, Hyunki, Mukherjee, Anubhav
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1901.07964

Abstract

We give several criteria on a closed, oriented 3-manifold that will imply that it is the boundary of a (simply connected) 4-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact 3-manifold, or contact 3-manifolds with non-vanishing Heegaard Floer invariant, is the boundary of a simply connected 4-manifolds that admits infinitely many distinct smooth structures each of which supports a symplectic structure with concave boundary, that is there are infinitely many exotic caps for any such contact manifold.

Related

• Diffeomorphisms of 4-manifolds with boundary and exotic embeddings
• Smooth structures on collarable ends of 4-manifolds
• 4-manifolds with boundary and fundamental group ℤ
• Nuclei and exotic 4-manifolds
• Exotic structures and adjunction inequality