## Theses and Dissertations--Mathematics

#### Author ORCID Identifier

https://orcid.org/0000-0001-5712-1784

2023

#### Degree Name

Doctor of Philosophy (PhD)

#### Document Type

Doctoral Dissertation

#### College

Arts and Sciences

Mathematics

Bertrand Guillou

#### Abstract

We provide the slice (co)towers of $$\Si{V} H_{C_2}\ul M$$ for a variety of $$C_2$$-representations $$V$$ and $$C_2$$-Mackey functors $$\ul M$$. We also determine a characterization of all 2-slices of equivariant spectra over the Klein four-group $$C_2\times C_2$$. We then describe all slices of integral suspensions of the equivariant Eilenberg-MacLane spectrum $$H\ulZ$$ for the constant Mackey functor over $$C_2\times C_2$$. Additionally, we compute the slices and slice spectral sequence of integral suspensions of $H\ulZ$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors $$\mpi_{k\rho} H_{K_4}\ulZ$$ and $\mpi_{k\rho} H_{Q_8}\ulZ$.

#### Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2023.020

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