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Harald Biller

Fixed points of pro-tori in cohomology spheres

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.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 05/2005
Pages: 479 - 492

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