The $ER(2)$-cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C}{P}^n$

Abstract

The $ER(2)$-cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C}{P}^n$ are computed along with the Atiyah-Hirzebruch spectral sequence for $ER(2{)}^{\ast }(\mathbb{C}{P}^{\infty })$. This, along with other papers in this series, gives us the $ER(2)$-cohomology of all Eilenberg-MacLane spaces. Since $ER(2)$ is $TM{F}_0(3)$ after a suitable completion, these computations also take care of that theory.

25 pages, version 2: minor changes to exposition, a few diagrams added. Comments welcome!

References in corpus (1)

• The ER(n)-cohomology of BO(q), and real Johnson-Wilson orientations for vector bundles

Cited by in corpus (1)

• The Real Johnson-Wilson Cohomology of $\mathbb{C}{P}^{\infty }$