The ER(2)-cohomology of X^nCP^\infty and BU(n)

TL;DR

This paper advances the computation of ER(2)-cohomology for complex projective space products and classifying spaces of unitary groups, addressing challenges due to non-complex orientability.

Contribution

It extends the computability of ER(2)-cohomology to new classes of spaces, overcoming difficulties posed by the theory's non-complex orientability.

Findings

Computed ER(2)-cohomology for (CP^∞)^n and BU(n)

Addressed challenges from non-complex orientability

Enhanced understanding of real Johnson-Wilson theory applications

Abstract

We continue the development of the computability of the second real Johnson-Wilson theory. As ER(2) is not complex orientable, this gives some difficulty even with basic spaces. In this paper we compute the second real Johnson-Wilson theory for products of infinite complex projective spaces and for the classifying spaces for the unitary groups.