Chow-Witt rings of Grassmannians

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 $\mathrm{BO}(n)$ with local coefficients, as done by Cadek. The computations of Chow-Witt rings of classifying spaces of ${\mathrm{GL}}_n$ 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.

Significant revision, streamlined proofs, 34p

References in corpus (3)

• An Arithmetic Count of the Lines on a Smooth Cubic Surface
• The real cycle class map
• Chow-Witt rings of classifying spaces for symplectic and special linear groups

Cited by in corpus (3)

• Aspects of enumerative geometry with quadratic forms
• The real cycle class map
• An arithmetic count of the lines meeting four lines in P^3