## Abstract

We describe the slice spectral sequence
of a 32-periodic ${C}_{4}$-spectrum ${K}_{[2]}$ related to the
${C}_{4}$ norm
${\mathrm{MU}}^{(({C}_{4}))}={N}_{{C}_{2}}^{{C}_{4}}{\mathrm{MU}}_{\mathbb{R}}$ of the real cobordism spectrum ${\mathrm{MU}}_{\mathbb{R}}$. We will give
it as a spectral sequence of Mackey functors converging to the graded Mackey
functor ${\underset{\xaf}{\pi}}_{*}{K}_{[2]}$, complete with differentials and exotic
extensions in the Mackey functor structure.
The slice spectral sequence for the 8-periodic real *K*-theory
spectrum ${K}_{\mathbb{R}}$ was first analyzed by Dugger. The ${C}_{8}$
analog of ${K}_{[2]}$ is 256-periodic and detects the Kervaire invariant
classes ${\theta}_{j}$. A partial analysis of its slice spectral
sequence led to the solution to the Kervaire invariant problem, namely
the theorem that ${\theta}_{j}$ does not exist for $j\ge 7$.

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.