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Nonexistence of smooth effective one fixed point actions of finite Oliver groups on low-dimensional spheres

Volume 66 / 2018

Agnieszka Borowiecka, Piotr Mizerka Bulletin Polish Acad. Sci. Math. 66 (2018), 167-177 MSC: Primary 57S17; Secondary 57S25. DOI: 10.4064/ba8150-9-2018 Published online: 28 September 2018

Abstract

According to Laitinen and Morimoto (1998), 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 $G=A_5\times C_p$, where $p=3,5,7$, we present a strategy of excluding smooth effective one fixed point $G$-actions on low-dimensional spheres.

Authors

  • Agnieszka BorowieckaFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    61-614 Poznań, Poland
    e-mail
  • Piotr MizerkaFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    61-614 Poznań, Poland
    e-mail

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