Abstract
Since 1946 it has been an open question which compact Lie groups can act smoothly on some sphere with exactly one fixed point. In this paper we solve the problem completely for finite groups: these groups are exactly those which can act smoothly on some disk without fixed points, a class determined by R. Oliver. Our main tools are the Burnside ring and the Grothendieck-Witt ring (classical to some extent) and a form of equivariant surgery theory allowing middle-dimensional singular sets developed recently.
| Original language | English |
|---|---|
| Pages (from-to) | 479-520 |
| Number of pages | 42 |
| Journal | Forum Mathematicum |
| Volume | 10 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jan 1 1998 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Cite this
Laitinen, E., & Morimoto, M. (1998). Finite groups with smooth one fixed point actions on spheres. Forum Mathematicum, 10(4), 479-520. https://doi.org/10.1515/form.10.4.479