On instanton homology of corks W_n

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 $τ$ on its boundary $Σ_n = \partial W_n$. We compute the instanton Floer homology of $Σ_n$ and show that the map induced on the instanton Floer homology by $τ: Σ_n \rightarrow Σ_n$ is non-trivial.

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