$TM{F}_0(3)$ Characteristic classes for String bundles

Abstract

We compute the completed $TM{F}_0(3)$ cohomology of the 7-connective cover $BString$ of $BO$. We use cubical structures on line bundles over elliptic curves to construct an explicit class which together with the Pontryagin classes freely generates the cohomology ring.

this version will be published in Math. Zeitschrift