发表机构
University of Massachusetts Amherst; Rényi Institute of Mathematics; Princeton University（马萨诸塞大学阿默斯特分校; 雷尼数学研究所; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
构造无穷多个同胚于CP²#7(-CP²)但两两不微分同胚的不可约光滑四流形，每个允许保定向自由对合；其商空间给出无穷多个基本群为Z/2Z、b₂=3的不可约定号四流形，填补地理学空白，方法基于新颖的等变环面手术。
AI 中文摘要
我们构造了无穷多个两两不微分同胚的不可约光滑四流形，它们同胚于 ${\mathbb {CP}}^2\\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$，且每个都允许一个保定向的自由对合。它们的商空间给出无穷多个具有基本群 ${\mathbb {Z}}/2 {\mathbb {Z}}$ 和 $b_2=3$ 的不可约定号四流形，填补了此类例子地理学中的相应空白。构造无穷多个不同例子依赖于一种新颖的等变环面手术。
英文摘要
We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifolds with fundamental group ${\mathbb {Z}}/2 {\mathbb {Z}}$ and $b_2=3$, filling the corresponding gap in the geography of such examples. The construction of infinitely many distinct examples relies on a novel equivariant torus surgery.
