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Finite groups with smooth one fixed point actions on spheres
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Erkki Laitinen
Published/Copyright:
March 2, 2009
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.
Received: 1996-10-20
Revised: 1997-05-13
Published Online: 2009-03-02
Published in Print: 1998-07-10
© Walter de Gruyter
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Articles in the same Issue
- Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients
- Radon transforms on the symmetric group and harmonic analysis of a class of invariant Laplacians
- Linear submanifolds and bisectors in ℂHn
- Affine Hughes groups acting on 4-dimensional compact projective planes
- A parallelism for contact conformal sub-Riemannian geometry
- Finite groups with smooth one fixed point actions on spheres
