2016/09/14 by Motoo Tange, Tange, Motoo · 1 citation
Mathematics · #57R55 #57R65 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1609.04344
openalex publication_date 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.