# Power operations and the Kunneth spectral sequence

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Sean Tilson, Wayne State University
Fine Hall 214

Power operations have been constructed and successfully utilized in the Adams and Homological Homotopy Fixed Point Spectral Sequences by Bruner and Bruner-Rognes. It was thought that such results were not specific to the spectral sequence, but rather that they arose because highly structured ring spectra are involved. In this talk, we show that the Kunneth Spectral Sequence enjoys some nice multiplicative properties, and use old computations of Steinberger's with our current work to compute operations in the homotopy of some relative smash products. We will end with an application of these computations to give a non-existence result for $E_{\infty}$ complex orientations of certain ring spectra.