具有非平凡$\hat{A}$ -亏格的$HP^2$ -丛
An $HP^2$-bundle over $S^4$ with nontrivial $\hat{A}$-genus
摘要：
我们解释了$S^4$上的光滑$HP^2$ -丛的存在性，它的全空间具有非平凡的$\hat{A}$ -亏格.结合一个参数回到希钦，这回答了一个问题的希克和暗示，空间的黎曼度量的正截面曲率的闭流形可以有非平凡的高理性同伦群。
英文摘要：
We explain the existence of a smooth $HP^2$-bundle over $S^4$ whose total space has nontrivial $\hat{A}$-genus. Combined with an argument going back to Hitchin, this answers a question of Schick and implies that the space of Riemannian metrics of positive sectional curvature on a closed manifold can have nontrivial higher rational homotopy groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
