# Enchiridion: Vol. 2 (2016): Vitaly Lorman

Author
Vitaly Lorman (Johns Hopkins University)

Source Paper
Landweber flat real pairs and $ER(n)$-cohomology
joint with Nitu Kitchloo and W. Stephen Wilson
(arxiv:1603.06865)

Source Paper Abstract
We take advantage of the internal algebraic structure of the Bockstein spectral sequence converging to $ER(n)^*(pt)$ to prove that for spaces $Z$ that are part of Landweber flat real pairs with respect to $E(n)$, the cohomology ring $ER(n)^*(Z)$ can be obtained from $E(n)^*(Z)$ by base change. In particular, our results allow us to compute the Real Johnson-Wilson cohomology of the Eilenberg-MacLane spaces $Z = K(\mathbb{Z}, 2m+1), K(\mathbb{Z}/2^q, 2m), K(\mathbb{Z}/2, m)$ for all integers $m$ and $q$, as well as connective covers of $BO$: $BO, BSO, BSpin$, and $BO$.