On instanton homology of corks Wₙ

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We consider a family of corks, denoted Wₙ, 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 Σₙ = ∂ Wₙ. We compute the instanton Floer homology of Σₙ and show that the map induced on the instanton Floer homology by τ: Σₙ → Σₙ is non-trivial.