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

Abstract

Using the Bockstein spectral sequence developed previously by the authors, we compute the ring ER(n)^*(BO(q)) explicitly. We then use this calculation to show that the ring spectrum MO[2^{n+1}] is ER(n)-orientable (but not ER(n+1)-orientable), where MO[2^{n+1}] is defined as the Thom spectrum for the self map of BO given by multiplication by 2^{n+1}.

References in corpus (2)

• On fibrations related to real spectra
• The Morava K-theory of BO(q) and MO(q)

Cited by in corpus (10)

• Gorenstein duality for Real spectra
• Landweber flat real pairs and ER(n)-cohomology
• The Real Johnson-Wilson Cohomology of $\mathbb{C}{P}^{\infty }$
• Tate blueshift and vanishing for Real oriented cohomology
• $TM{F}_0(3)$ Characteristic classes for String bundles
• The $ER(2)$-cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C}{P}^n$
• On the $\mathrm{EO}$-orientability of vector bundles
• The ER(2)-cohomology of X^nCP^\infty and BU(n)
• Vanishing lines in chromatic homotopy theory
• The Real-oriented cohomology of infinite stunted projective spaces