论文标题
改进的四个周期定理和对称性的HOPF猜想
An improved four-periodicity theorem and a conjecture of Hopf with symmetry
论文作者
论文摘要
在1930年代，H. hopf猜想正面截面曲率的封闭，均匀的歧管具有正极特征。我们在歧管上的等距$ t^4 $ Action的其他假设下显示了这一点，从肯纳德，Wiemeler和Wilking的先前定理提高了，假设$ t^5 $ - action。更具体地说，这是通过对可能的固定点成分进行合理的共同体分类来实现的。主要的新工具是对肯纳德最初通过使用特征类理论开发的四个周期定理的改进。作为第二个应用程序，我们对封闭的弯曲式弯曲式歧管进行了合理的共同体分类，而无需奇怪的理性共同体学，可以接受等距$ t^6 $ -ACTION。
In the 1930s, H. Hopf conjectured that a closed, even-dimensional manifold of positive sectional curvature has positive Euler characteristic. We show this under the additional assumption of an isometric $T^4$-action on the manifold, improving from previous theorems of Kennard, Wiemeler and Wilking assuming a $T^5$-action. More specifically, this is achieved by giving a rational cohomology classification of possible fixed point components. The main new tool is an improvement on the four-periodicity theorem originally developed by Kennard through the use of characteristic class theory. As a second application we give a rational cohomology classification of closed positively curved even-dimensional manifolds without odd rational cohomology that admit an isometric $T^6$-action.
