AI 中文总结
本文证明高局部化 $\widehat{A}$-亏格作为正纯量曲率障碍时，可去掉不动点集连通性和群元素正则性两个假设。
AI 中文摘要
对于有限生成离散群 $\Gamma$ 在自旋流形 $M$ 上的真余紧作用，作者与 Mathai 先前引入的高局部化 $\widehat{A}$-亏格 $\widehat{A}_g(M,\omega)$ 被证明是 $\Gamma$-不变正纯量曲率度量的障碍，其中 $\omega$ 来自 $H^*(\underline{B}\Gamma,\mathbb{R})$ 的子环，该子环由次数至多为 $2$ 的元素生成，且假设不动点集 $M^g$ 连通并且 $g$ 关于某个实群 $2$-上循环是正则的。我们证明这两个假设均可去掉。
英文摘要
For a proper cocompact action of a finitely generated discrete group $Γ$ on a spin manifold $M$, the higher localised $\widehat{A}$-genera $\widehat{A}_g(M,ω)$ introduced earlier by the author and Mathai were shown to be an obstruction to $Γ$-invariant metrics of positive scalar curvature, for $ω$ arising from the subring of $H^*(\underline{B}Γ,\mathbb{R})$ generated by elements of degree at most $2$, under the assumptions that the fixed-point set $M^g$ is connected and that $g$ is regular with respect to a certain real group $2$-cocycle. We show that both assumptions can be dropped.
Comments9 pages
