Abstract

Let $X$ be a smooth, closed 4-manifold which is homotopy equivalent to $S^2\times S^2$. By the Seiberg-Witten theory, we take $\mathrm{Ind}_{A_5}D_X$ as a virtual $A_5$-representation and give its concrete representation.
We also study $\mathrm{Ind}_{A_5}D_X$ when $X$ is homotopy equivalent to $\sharp_n S^2 \times S^2$. Besides we give an example of our main theorem.

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