The Laitinen Conjecture for finite solvable Oliver groups

Pawałowski, Krzysztof; Sumi, Toshio

doi:10.1090/S0002-9939-09-09719-6

The Laitinen Conjecture for finite solvable Oliver groups
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by Krzysztof Pawałowski and Toshio Sumi PDF

Proc. Amer. Math. Soc. 137 (2009), 2147-2156 Request permission

Abstract:

For smooth actions of $G$ on spheres with exactly two fixed points, the Laitinen Conjecture proposed an answer to the Smith question about the $G$-modules determined on the tangent spaces at the two fixed points. Morimoto obtained the first counterexample to the Laitinen Conjecture for $G = \textrm {Aut}(A_6)$. By answering the Smith question for some finite solvable Oliver groups $G$, we obtain new counterexamples to the Laitinen Conjecture, presented for the first time in the case where $G$ is solvable.

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