Abstract. We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S 5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.
Let M be a closed, connected, orientable topological
$4$
-manifold, and G be a finite group acting topologically and locally linearly on M. In this paper, we investigate the spectral sequence for the Borel cohomology
$H^*_G(M)$
and establish new bounds on the rank of G for homologically trivial actions with discrete singular set.
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