Multiplicative structure on Real Johnson-Wilson theory

Abstract

We prove that the Real Johnson-Wilson theories ER(n) are homotopy associative and commutative ring spectra up to phantom maps. We further show that ER(n) represents an associatively and commutatively multiplicative cohomology theory on the category of (possibly non-compact) spaces.

arXiv comment16 pages, version 2. Added a new section revisiting $ER(n)$-orientations of vector bundles and minor improvements to exposition. To appear in Proceedings of the Mid-Atlantic Topology Conference