Let G be $$A_5$$, $$A_4$$, or a finite group with cyclic Sylow 2 subgroup. We show that every closed smooth G manifold M has a strongly algebraic model. This means, there exist a nonsingular real algebraic G variety X which is equivariantly diffeomorphic to M and all G vector bundles over X are strongly algebraic. Making use of improved blow-up techniques and the literature on equivariant bordism theory, we are extending older algebraic realization results.

中文翻译：

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一些有限群动作的代数实现

令 G 为 $$A_5$$、$$A_4$$ 或具有循环 Sylow 2 子群的有限群。我们表明每个封闭的光滑 G 流形 M 都有一个强代数模型。这意味着，存在一个非奇异实代数 G 簇 X，它与 M 等变微分，并且 X 上的所有 G 向量丛都是强代数的。利用改进的放大技术和等变边主义理论的文献，我们正在扩展旧的代数实现结果。