On the spectrum $b\mathrm{o}\wedge tmf$

Abstract

M. Mahowald, in his work on $b\mathrm{o}$-resolutions, constructed a $b\mathrm{o}$-module splitting of the spectrum $b\mathrm{o}\wedge b\mathrm{o}$ into a wedge of summands related to integral Brown-Gitler spectra. In this paper, a similar splitting of $b{\rm o} \sm tmf$ is constructed. This splitting is then used to understand the $b{\mathrm{o}}_{\ast }$-algebra structure of $b{\mathrm{o}}_{\ast }tmf$ and allows for a description of $b{\mathrm{o}}^{\ast }tmf$.

15 pages, 4 figures