The Laitinen Conjecture for finite solvable Oliver groups

Abstract

For smooth actions of G G on spheres with exactly two fixed points, the Laitinen Conjecture proposed an answer to the Smith question about the G G -modules determined on the tangent spaces at the two fixed points. Morimoto obtained the first counterexample to the Laitinen Conjecture for G = Aut ( A 6 ) G = \textrm {Aut}(A_6) . By answering the Smith question for some finite solvable Oliver groups G G , we obtain new counterexamples to the Laitinen Conjecture, presented for the first time in the case where G G is solvable.