论文标题
捆绑捆绑$ \ hat {a} $ - 属和曲率较低的指标空间
Bundles with non-multiplicative $\hat{A}$-genus and spaces of metrics with lower curvature bounds
论文作者
论文摘要
我们用两个球的基础和纤维产品构建光滑的捆绑包，其总空间的$ \ hat {a} $ - 属。然后，我们使用这些捆绑包来定位所有弯曲度较低的riemannian指标空间的非平凡合理同型组群，用于所有尺寸六个或至少十个的自旋manifolds，这些旋转模型承认了这样的度量，并且是一个相互连接的一定总和，具有一定的一定程度和$ s^n \ s^n \ times s^n $ s^n $ s^n $ s^n $ s^n \ times s^n \ time s^n \ n \ n \ n \ n \ n+n+n+1}我们还构建了$ m $的歧管$ m $，其riemannian积极标态曲率的指标具有同质组群，其中包含无限顺序的元素，这些元素属于$ m $ diffeemormorphism group的推动行动所引起的轨道图的图像。
We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with lower curvature bounds for all Spin-manifolds of dimension six or at least ten which admit such a metric and are a connected sum of some manifold and $S^n \times S^n$ or $S^n \times S^{n+1}$, respectively. We also construct manifolds $M$ whose spaces of Riemannian metrics of positive scalar curvature have homotopy groups that contain elements of infinite order which lie in the image of the orbit map induced by the push-forward action of the diffeomorphism group of $M$.
