AI 中文总结
本文证明 Cartwright-Steger 曲面的实商为闭定向光滑四流形，同胚于 CP^2#(S^1×S^3)，并给出其作为双重分支覆盖的结构。
AI 中文摘要
Borisov 和 Yeung 证明了 Cartwright-Steger 曲面 $X$ 定义在 ${\mathbb {Q}}$ 上，因此复共轭给出 $X$ 上的反全纯对合。我们证明轨道空间 $Y$ 是一个闭定向光滑四流形，同胚于 ${\mathbb {CP}}^2\\# (S^1 \times S^3)$，并将 $X$ 表示为双重分支覆盖 $X\to Y$，其分支轨迹微分同胚于三个实射影平面的连通和。
英文摘要
Borisov and Yeung showed that the Cartwright-Steger surface $X$ is defined over ${\mathbb {Q}}$, hence complex conjugation gives an antiholomorphic involution on $X$. We show that the orbit space $Y$ is a closed oriented smooth four-manifold homeomorphic to ${\mathbb {CP}}^2\# (S^1 \times S^3)$, presenting $X$ as a double branched cover $X\to Y$, with branch locus diffeomorphic to the connected sum of three copies of the real projective plane.
Comments13 pages, added remark about diffeomorphism type
