论文标题
$ hp^2 $ -Bundle $ s^4 $与非平凡$ \ hat {a} $ - 属
An $HP^2$-bundle over $S^4$ with nontrivial $\hat{A}$-genus
论文作者
论文摘要
我们解释了平滑的$ hp^2 $ -Bundle在$ s^4 $上，其总空间具有非平凡的$ \ hat {a} $ - 属。结合回到希钦（Hitchin）的论点，这回答了一个奇克（Schick）的问题，并意味着在封闭的歧管上积极截面曲率的riemannian指标的空间可以具有非平凡的较高理性同型组。
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.
