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Chow–Witt rings of Grassmannians

Matthias Wendt

Algebraic & Geometric Topology 24 (2024) 1–48
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 BO(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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