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On the length of cohomology spheres
Topology and its Applications ( IF 0.6 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.topol.2020.107569
Denise de Mattos , Edivaldo L. dos Santos , Nelson Antonio Silva

We present the length, a numerical cohomological index theory, of $ G $-spaces which are cohomology spheres and $ G $ is a $p$-torus or a torus group, where $p$ is a prime. As a consequence, we obtain Borsuk-Ulam and Bourgin-Yang type theorems in this context. A sharper version of the Bourgin-Yang theorem for topological manifolds is also proved. Also, we give some general results regarding the upper and lower bound for the length.

中文翻译:

关于上同调球的长度

我们提出了作为上同调球体的 $G$-空间的长度,一种数值上同调指数理论,$G$ 是一个 $p$-环面或一个环面群,其中 $p$ 是素数。因此,我们在此上下文中获得 Borsuk-Ulam 和 Bourgin-Yang 型定理。还证明了拓扑流形的 Bourgin-Yang 定理的更清晰版本。此外,我们还给出了一些关于长度上限和下限的一般结果。
更新日期:2020-12-01
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