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Fixed points of pro-tori in cohomology spheres
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Harald Biller
Veröffentlicht/Copyright:
27. Juli 2005
Abstract
Essential results from the theory of torus actions, initiated by P. A. Smith, are generalized to actions of pro-tori, i.e. compact connected abelian groups. We show that the fixed point set in a (rational cohomology) manifold, resp. sphere, is a rational cohomology manifold, resp. sphere, of even codimension. Borel’s dimension formula for the fixed spheres of codimension one subgroups is proved for actions of pro-tori on (cohomology) spheres. This yields a sharp upper bound for the group dimension. Finally, we describe some applications to actions of pro-tori on compact generalized polygons.
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Published Online: 2005-07-27
Published in Print: 2005-05-25
© de Gruyter
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Artikel in diesem Heft
- Feller-type properties and path regularities of Markov processes
- Equivalent expressions for norms in classical Lorentz spaces
- Modular arithmetic of free subgroups
- Complete polynomial vector fields in two complex variables
- 3-dimensional Bol loops as sections in non-solvable Lie groups
- Sharp conditions for weighted Sobolev interpolation inequalities
- Fixed points of pro-tori in cohomology spheres
- Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions
- A locally finite dense group acting on the random graph
Artikel in diesem Heft
- Feller-type properties and path regularities of Markov processes
- Equivalent expressions for norms in classical Lorentz spaces
- Modular arithmetic of free subgroups
- Complete polynomial vector fields in two complex variables
- 3-dimensional Bol loops as sections in non-solvable Lie groups
- Sharp conditions for weighted Sobolev interpolation inequalities
- Fixed points of pro-tori in cohomology spheres
- Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions
- A locally finite dense group acting on the random graph
