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

Authors: Ian Hambleton and Ergün Yalçın
Journal: Trans. Amer. Math. Soc. 368 (2016), 5951-5977
MSC (2010): Primary 20J05, 55U15, 57S17, 18Gxx
DOI: https://doi.org/10.1090/tran/6567
Published electronically: October 20, 2015
MathSciNet review: 3458403
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Abstract: Let be a rank two finite group, and let $\mathcal {H}$ denote the family of all rank one -subgroups of for which $\operatorname {rank}_p(G)=2$ . We show that a rank two finite group which satisfies certain explicit group-theoretic conditions admits a finite -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 -CW-complex examples.

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