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cohomology

# Contents

## Idea

The 2-periodic ring spectrum-version of the sphere spectrum. It is formed by taking the Thom spectrum of the $E_2$ map

$\mathbb{Z} \;\simeq\; \Omega^2 B U(1) \longrightarrow \Omega^2 B U \longrightarrow B U \times \mathbb{Z} \,,$

where the last map is specified by Bott periodicity (Lurie, Rotation Invariance, Remark 3.5.13). It cannot be equipped with an $E_{\infty}$ structure.

As a spectrum it is given by the direct sum (wedge sum) $\bigoplus_{n \in \mathbb{Z}} \mathbb{S}^{-2n}$ of all even-degree suspensions of the plain sphere spectrum.

## References

Last revised on September 10, 2021 at 10:20:05. See the history of this page for a list of all contributions to it.