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arXiv · 1805.06142

Chow-Witt rings of Grassmannians

Matthias Wendt
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Abstract

We complement our previous computation of the Chow-Witt rings of classifying spaces of special linear groups by an analogous computation for the general linear groups. This case involves discussion of non-trivial dualities. The computation proceeds along the lines of the classical computation of the integral cohomology of ${\rm BO}(n)$ with local coefficients, as done by Cadek. The computations of Chow-Witt rings of classifying spaces of ${\rm GL}_n$ are then used to compute the Chow-Witt rings of the finite Grassmannians. As before, the formulas are close parallels of the formulas describing integral cohomology rings of real Grassmannians.

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Matthias Wendt. 2020-03-23. Chow-Witt rings of Grassmannians. https://doi.org/10.2140/agt.2024.24.1

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