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Nonexistence of Smooth Effective One Fixed Point Actions of Finite Oliver Groups on Low-dimensional Spheres
A. Borowiecka, P. Mizerka
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According to the work of Laitinen, Morimoto, Oliver and Pawa\l{}owski, a finite group G has a smooth effective one fixed point action on some sphere if and only if G is an Oliver group. For some finite Oliver groups G of order up to $216$, and for G=A₅×Cₙ for n=3,5,7, we present a strategy of excluding of smooth effective one fixed point G-actions on low-dimensional spheres.
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