One stabilization is not enough for contractible 4-manifolds

TL;DR

This paper constructs a specific example of a cork in 4-manifold topology that remains exotic even after stabilization with S^2 x S^2, demonstrating limitations of stabilization in simplifying exotic structures.

Contribution

It provides the first explicit example of a cork that stays exotic after a connected sum with S^2 x S^2, advancing understanding of exotic 4-manifolds.

Findings

Existence of a cork that remains exotic after stabilization

An exotic pair of contractible 4-manifolds persists after S^2 x S^2 stabilization

Limits of stabilization techniques in 4-manifold topology

Abstract

We construct an example of a cork that remains exotic after taking a connected sum with $S^2 \times S^2$. Combined with a work of Akbulut-Ruberman, this implies the existence of an exotic pair of contractible 4-manifolds which remains absolutely exotic after taking a connected sum with $S^2 \times S^2$.