Group actions on spheres with rank one isotropy

Abstract

Let G be a rank two finite group, and let $\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\cH$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear G-CW-complex examples.

26 pages. Trans. Amer. Math. Soc. (final version); sequel to "Homotopy Representations over the Orbit Category", Homology, Homotopy and Applications (arXiv:1402.3306)