An infinite order cork

TL;DR

This paper constructs an infinite order cork in 4-manifold topology, demonstrating a sequence of distinct smooth structures generated by iterated boundary diffeomorphisms.

Contribution

It introduces the first example of an infinite order cork, expanding understanding of smooth structures in 4-manifolds.

Findings

Constructed an infinite order cork (W,f) with Stein structure.

Generated infinitely many distinct smooth structures via iterated boundary diffeomorphisms.

Shows the existence of infinite order corks in 4-manifold topology.

Abstract

We construct an infinite order cork (W,f), which means that W is a smooth compact contractible 4-manifold with Stein structure, and f is a self diffeomorphism of the boundary of W, such that the n-fold composition maps f^{n}=f o f o... o f give rise to smoothly distinct corks (W, f^{n}) for sufficiently large values of n, as it approaches to infinity.