正数量曲率的Gromoll滤子、KO-特征类和度量
The Gromoll filtration, KO-characteristic classes and metrics of positive scalar curvature
摘要：
设X是一个m维闭自旋流形，X上存在一个正数量曲率度量，Pos（X）是所有度量的空间.对于Pos（X）中的任意g，Hitchin利用KO-值α-不变量定义了从π_{n-1}（Pos（X）到KO_{m+n}的同态A_{n-1}.然后，他表明，A_0是不是0，如果m = 8 k或8 k +1和A_1是不是0，如果m = 8 k-1或8$。在本文中，我们使用Hitchin的方法，并通过证明A_{8j+1-m}是不为0时，m>6和8 j- m >= 0，推广这些结果。新的输入是在群Γ^{n+1} = π_0（\Diff（D^n，\del））的Gromoll过滤中具有非平凡α不变的元素。我们证明了当j>0时，α（Γ^{8 j +2}_{8 j-5}）不为0.关于存在于Gromoll过滤深处的元素的信息是本说明的第二个主要新结果。
英文摘要：
Let X be a closed m-dimensional spin manifold which admits a metric of positive scalar curvature and let Pos(X) be the space of all such metrics. For any g in Pos(X), Hitchin used the KO-valued alpha-invariant to define a homomorphism A_{n-1} from π_{n-1}(Pos(X) to KO_{m+n}. He then showed that A_0 is not 0 if m = 8k or 8k+1 and that A_1 is not 0 if m = 8k-1 or 8$. In this paper we use Hitchin's methods and extend these results by proving that A_{8j+1-m} is not 0 whenever m>6 and 8j - m >= 0. The new input are elements with non-trivial alpha-invariant deep down in the Gromoll filtration of the group Γ^{n+1} = π_0(\Diff(D^n, \del)). We show that α(Γ^{8j+2}_{8j-5}) is not 0 for j>0. This information about elements existing deep in the Gromoll filtration is the second main new result of this note.
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。
