论文标题
在$ \ mathbb {z} _2 \ oplus \ mathbb {z} _2 $ - 米对称空间
Equivariant formality of the isotropy action on $\mathbb{Z}_2\oplus \mathbb{Z}_2$-symmetric spaces
论文作者
论文摘要
紧凑的对称空间可能是最突出的形式空间之一，即理性同拷贝类型是理性共同体学代数的正式后果的空间。作为概括，甚至知道他们的各向同性作用是正式的。 在本文中，我们表明$（\ mathbb {z} _2 \ oplus \ mathbb {z} _2）$ - 对称空间在沙利文（Sullivan）的意义上是等上正式的和正式的。此外，在对称空间的情况下，我们以新方法为对称空间提供了一个简短的替代证明。
Compact symmetric spaces are probably one of the most prominent class of formal spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational cohomology algebra. As a generalisation, it is even known that their isotropy action is equivariantly formal. In this article we show that $(\mathbb{Z}_2\oplus \mathbb{Z}_2)$-symmetric spaces are equivariantly formal and formal in the sense of Sullivan, in particular. Moreover, we give a short alternative proof of equivariant formality in the case of symmetric spaces with our new approach.
