Non-existence theorems on infinite order corks

Suppose that X, X' are simply-connected closed exotic 4 manifolds. It is well-known that X' is obtained by an order 2 cork twist of X. We give an infinite family of exotic 4-manifolds not generated by any infinite order cork. This is the first example admitting such a condition. We prove a necessary condition of 4-dimensional Ozsvath-Szabo invariants for a family to be generated by an infinite order cork and as an application give non-contractible relatively exotic 4-manifolds that are never induced by any cork. Furthermore, we give an estimate of the number of Ozsvath-Szabo invariants of 4-manifolds generated by a cork.& COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

Suppose X and X' are simply-connected closed exotic 4 manifolds. X' is obtained by an order 2 cork twist of X. An infinite family of exotic 4-manifolds not generated by any infinite order cork is given, providing the first example of such a condition. A necessary condition of 4-dimensional Ozsvath-Szabo invariants for a family to be generated by an infinite order cork is proven, and non-contractible relatively exotic 4-manifolds that are never induced by any cork are presented as an application. Furthermore, an estimate of the number of Ozsvath-Szabo invariants of 4-manifolds generated by a cork is provided.