Physical Sciences and Mathematics Commons^™

Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications, Sean Michael Tilson

Wayne State University Dissertations

We construct Power operations in the K"unneth spectral sequence and the $C_2$ equivariant Adams spectral sequence. While the operations in the K"unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having $E_infty$ ring maps. The operations in the $C_2$-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory.