Generalized group characters and complex-oriented cohomology theories

Paul Pearson (Northwestern)

The ring of complex representations with rational coefficients of a finite group G can be naturally identified with the ring of class functions from G to L (where L is an extension of the rationals Q) that are invariant under the action of the Galois group Gal(L/Q). In this talk, we discuss the generalizations by Hopkins, Kuhn, and Ravenel that extend this result about the complex representation ring R(G) to analogous results about the group cohomology ring E^*(BG) and the equivariant cohomology ring E^*(EG ×_G X).

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