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