Euler class groups and 2-torsion elements

Bhatwadekar, S. M.; Fasel, Jean; Sane, Sarang

doi:10.1016/j.jpaa.2013.04.016

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…In particular, the top Stiefel-Whitney classes of any bundle (satisfying the conditions in the statement) vanishes automatically. This also complements the example discussed in [BFS14]. Note that our methods do not apply directly to their example, which has 2-torsion in the Chow-groups, but the above argument at least implies vanishing of e n ∈ H n (U, I n ) for the variety U in loc.cit.…”

Section: Now Consider the Diagramsupporting

confidence: 60%

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Chow–Witt rings of classifying spaces for symplectic and special linear groups

Hornbostel

Wendt

2019

Journal of Topology

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We compute the Chow-Witt rings of the classifying spaces for the symplectic and special linear groups. In the structural description we give, contributions from real and complex realization are clearly visible. In particular, the computation of cohomology with I j -coefficients is done closely along the lines of Brown's computation of integral cohomology for special orthogonal groups. The computations for the symplectic groups show that Chow-Witt groups are a symplectically oriented ring cohomology theory. Using our computations for special linear groups, we also discuss the question when an oriented vector bundle of odd-rank splits off a trivial summand. Contents

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Section: Now Consider the Diagramsupporting

confidence: 60%

“…This also complements the example discussed in . Note that our methods do not apply directly to their example, which has 2‐torsion in the Chow‐groups, but the above argument at least implies vanishing of

{prefixe}_{n} \in {prefixH}^{n} false(U, I^{n} false)

for the variety

U

in .…”

Section: Euler Classes For Odd‐rank Modulessupporting

confidence: 51%

Chow–Witt rings of classifying spaces for symplectic and special linear groups

Hornbostel

Wendt

2019

Journal of Topology

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“…Indeed, K MW 0 (k) is not a PID and the only a priori structure of the image is that it is a K MW 0 (k)-submodule of K MW 0 (k). We refer to [5] for some computations in this direction, and we note that it would be interesting to compute some Milnor-Witt degrees of hypersurfaces in P n .…”

Section: Push-forwardsmentioning

confidence: 99%

Lectures on Chow-Witt groups

Fasel¹

2020

Motivic Homotopy Theory and Refined Enumerative Geometry

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Variations in 𝔸1 on a Theme of Mohan Kumar

Wendt

2019

International Mathematics Research Notices

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For every prime $p$, Mohan Kumar constructed examples of stably free modules of rank $p$ on suitable $p+1$-dimensional smooth affine varieties. This note discusses how to detect the corresponding unimodular rows by an explicit motivic cohomology group. Using the recent developments in the $\mathbb{A}^1$-obstruction classification of vector bundles, this provides an alternative proof of non-triviality of Mohan Kumar’s stably free modules. The reinterpretation of Mohan Kumar’s examples also allows to produce interesting examples of stably trivial torsors for other algebraic groups.

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Euler class groups and 2-torsion elements

Cited by 3 publications

References 15 publications

Chow–Witt rings of classifying spaces for symplectic and special linear groups

Chow–Witt rings of classifying spaces for symplectic and special linear groups

Lectures on Chow-Witt groups

Variations in 𝔸1 on a Theme of Mohan Kumar

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