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

Autor(en): Hornbostel, Jens
Wendt, Matthias
Stichwörter: 14C17 (primary); 14F42; 19D45; 19G12; 55R40 (secondary); AFFINE; FUNDAMENTAL IDEAL; Mathematics; OPERATIONS; POWERS; VECTOR-BUNDLES
Erscheinungsdatum: 2019
Herausgeber: WILEY
Journal: JOURNAL OF TOPOLOGY
Volumen: 12
Ausgabe: 3
Startseite: 916
Seitenende: 966
Zusammenfassung: 
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 Ij-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.
ISSN: 17538416
DOI: 10.1112/topo.12103

Show full item record

Page view(s)

3
Last Week
0
Last month
0
checked on Mar 1, 2024

Google ScholarTM

Check

Altmetric