On instanton homology of corks W_n

TL;DR

This paper computes the instanton Floer homology of a family of cork boundaries and demonstrates that the boundary twist induces a non-trivial map, revealing new insights into exotic smooth structures on 4-manifolds.

Contribution

It provides the first computation of instanton Floer homology for the corks W_n and shows the boundary twist acts non-trivially on this homology.

Findings

Instanton Floer homology of Σ_n is computed.

The boundary twist map τ induces a non-trivial automorphism.

Results contribute to understanding exotic smooth structures on 4-manifolds.

Abstract

We consider a family of corks, denoted $W_n$, constructed by Akbulut and Yasui. Each cork gives rise to an exotic structure on a smooth 4-manifold via a twist $\tau$ on its boundary $\Sigma_n = \partial W_n$. We compute the instanton Floer homology of $\Sigma_n$ and show that the map induced on the instanton Floer homology by $\tau: \Sigma_n \rightarrow \Sigma_n$ is non-trivial.