Group actions on spheres with rank one isotropy

Hambleton, Ian; Yalçın, Ergün

doi:10.1090/tran/6567

Group actions on spheres with rank one isotropy
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by Ian Hambleton and Ergün Yalçın PDF

Trans. Amer. Math. Soc. 368 (2016), 5951-5977 Request permission

Abstract:

Let $G$ be a rank two finite group, and let $\mathcal {H}$ denote the family of all rank one $p$-subgroups of $G$ for which $\operatorname {rank}_p(G)=2$. We show that a rank two finite group $G$ which satisfies certain explicit group-theoretic conditions admits a finite $G$-CW-complex $X\simeq S^n$ with isotropy in $\mathcal {H}$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear $G$-CW-complex examples.

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