#### Title

Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications

#### Access Type

Open Access Dissertation

#### Date of Award

January 2013

#### Degree Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Mathematics

#### First Advisor

Robert R. Bruner

#### Abstract

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.

#### Recommended Citation

Tilson, Sean Michael, "Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications" (2013). *Wayne State University Dissertations*. 800.

http://digitalcommons.wayne.edu/oa_dissertations/800