Non-existence theorems on infinite order corks

Abstract

Suppose that $X,X^{\prime }$ are simply-connected closed exotic 4-manifolds. It is well-known that $X^{\prime }$ is obtained by an order 2 cork twist of $X$. We give an infinite exotic family of 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 OS-invariants for a family to be generated by an infinite order cork and give non-contractible relatively exotic 4-manifolds that are never induced by any cork. Furthermore, we prove an estimate of the number of OS-invariants of 4-manifolds generated by a cork.

17 pages, 6 figures

References in corpus (1)

• On infinite order corks

Cited by in corpus (2)

• Nonexistence of twists and surgeries generating exotic 4-manifolds
• Infinite nonabelian corks