The Chow--Witt rings of the classifying space of quadratically oriented bundles

Abstract

In this paper we compute the Chow--Witt rings of the classifying space ${\mathrm{BSL}}_n^c$ of quadratically oriented vector bundles of rank $n$. We also discuss the corresponding quadratically-oriented cobordism spectrum ${\mathrm{MSL}}^c$ and show that it is equivalent to $\mathrm{MSL}$ after inverting $\eta$.

48 pages, comments welcome!