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

Etnyre, John; Min, Hyunki; Mukherjee, Anubhav

doi:10.1090/tran/8586

On $3$-manifolds that are boundaries of exotic $4$-manifolds
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by John B. Etnyre, Hyunki Min and Anubhav Mukherjee PDF

Trans. Amer. Math. Soc. 375 (2022), 4307-4332 Request permission

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 $3$-manifold with non-vanishing Heegaard Floer invariant, is the boundary of a simply connected $4$-manifold 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.

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