Multiplicative structure on Real Johnson-Wilson theory

TL;DR

This paper proves that the Real Johnson-Wilson theories ER(n) are homotopy associative and commutative ring spectra, establishing their role as multiplicative cohomology theories on various spaces.

Contribution

It demonstrates that ER(n) theories are homotopy associative and commutative ring spectra, and that they serve as multiplicative cohomology theories on a broad class of spaces.

Findings

ER(n) are homotopy associative and commutative ring spectra

ER(n) defines a multiplicative cohomology theory on non-compact spaces

The results hold up to phantom maps

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.