Chow–Witt rings of Grassmannians

Wendt, Matthias

doi:10.2140/agt.2024.24.1

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Chow–Witt rings of Grassmannians

Matthias Wendt

Algebraic & Geometric Topology 24 (2024) 1–48

DOI: 10.2140/agt.2024.24.1

Abstract

We complement the 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 nontrivial dualities. The computation proceeds along the lines of the classical computation of the integral cohomology of $B O (n)$ with local coefficients, as done by Čadek. The computations of Chow–Witt rings of classifying spaces of ${GL}_{n}$ 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.

Keywords

Chow–Witt rings, classifying spaces, vector bundles, characteristic classes, Grassmannians

Mathematical Subject Classification 2010

Primary: 14C15, 14F43

Secondary: 14C17, 14M15

References

Publication

Received: 25 March 2020

Revised: 24 July 2022

Accepted: 20 September 2022

Published: 18 March 2024

Authors

Matthias Wendt
Fachgruppe Mathematik und Informatik Bergische Universität Wuppertal Wuppertal Germany

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Volume 24, issue 1 (2024)