Equivariant J-groups of Complex Projective Spaces
by
Turgut Onder
Middle East Technical University

The group Sph X of spherical fibrations over a topological space X and the image JO(X) of the J-homomorphism J:KO(X) --> Sph(X), as well their equivariant analogues Sph_G X and JO_G(X), are of great importance in Homotopy Theory and Differential Topology.

For instance if we take X to be a projective space (either real, complex or quaternionic), then the resulting groups JO(X) holds the key to classical questions about the existence of cross sections of appropriate Stiefel fibrations. Similar things are true for equivariant JO- groups and equivariant cross sections of Stiefel fibrations.

In this anouncement we are going to present some formulae about the orders of elements of JO_G-groups of complex projective spaces for finite groups G which has no quaternionic type representations (this family covers e.g. all finite abelian groups). Parallel results for real projective spaces were obtained by J.C. Becker and U. Namboodiri back in 1970's and 80's.

Date received: June 30, 2000