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- W4297066475 abstract "A space is defined to be $n$-spheroidal if it has the homotopy type of an $n$-dimensional CW-complex $X$ with $H_{n}(X, mathbb{Z})$ not zero and finitely generated. A group $G$ is called $n$-spheroidal if its classifying space $K(G,1)$ is $n$-spheroidal. Examples include fundamental groups of compact manifold $K(G,1)$'s. Moreover, the class of groups $G$ which are $n$-spheroidal for some $n$, is closed under products, free products, and group extensions. If $Y$ is a space with $pi_{1}(Y)$ $n$-spheroidal, and if $H_{k}(Y;mathbb{F}_{p})$ is non-zero and finitely generated, and if $H_{i}(Y;mathbb{F}_{p}) = 0$ for $i>k$, then $H_{n+k}(overline{Y};mathbb{F}_{p}) neq 0$ for $overline{Y}$ a finite sheeted covering space of $Y$. Hence, dim$(Y) geq n+k$. Thus, it follows that if dim$(Y) < n$, and if $H_{k}(Y;mathbb{F}_{p}) neq 0$ and $H_{i}(Y;mathbb{F}_{p}) = 0$ for $i>k>0$, then $H_{k}(Y;mathbb{F}_{p})$ is not finitely generated. Similar results follow for $Ysubset K(G,1)$." @default.
- W4297066475 created "2022-09-26" @default.
- W4297066475 creator A5071763471 @default.
- W4297066475 date "2016-05-08" @default.
- W4297066475 modified "2023-10-16" @default.
- W4297066475 title "Spheroidal groups, virtual cohomology and lower dimensional G-spaces" @default.
- W4297066475 doi "https://doi.org/10.48550/arxiv.1605.02387" @default.
- W4297066475 hasPublicationYear "2016" @default.
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