On 3-manifolds that are boundaries of exotic 4-manifolds
Geometric Topology
2021-11-19 v3 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.1901.07964,
title = {On 3-manifolds that are boundaries of exotic 4-manifolds},
author = {John B. Etnyre and Hyunki Min and Anubhav Mukherjee},
journal= {arXiv preprint arXiv:1901.07964},
year = {2021}
}
Comments
26 pages, 2 figures. Minor updates to the text