group cohomology, nonabelian group cohomology, Lie group cohomology
Hochschild cohomology, cyclic cohomology?
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The 2-periodic ring spectrum-version of the sphere spectrum. It is formed by taking the Thom spectrum of the $E_2$ map
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.
Jacob Lurie, Rotation Invariance in Algebraic K-Theory, (pdf)
Mohammed Abouzaid, Andrew J. Blumberg, A.2.3 in: Arnold Conjecture and Morava K-theory (arXiv:2103.01507).
Last revised on September 10, 2021 at 10:20:05. See the history of this page for a list of all contributions to it.