We prove that for 4-manifolds M with residually finite fundamental group and non-spin universal covering M̃, the inequality dimmcM̃ ≤ 3 implies the inequality dimmcM̃ ≤ 2. This allows us to complete the proof of Gromov’s Conjecture for 4-manifolds with abelian fundamental group.

中文翻译：

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论非自旋四流形的宏观维度

我们证明对于 4 流形米具有剩余有限基本群和非自旋通用覆盖米̃, 不等式暗淡米C米̃ ≤ 3意味着不等式暗淡米C米̃ ≤ 2. 这使我们能够完成对具有阿贝尔基本群的 4 流形的格罗莫夫猜想的证明。