Degree three invariants for semisimple groups of types $B$, $C$, and $D$

TL;DR

This paper classifies degree 3 cohomological invariants for split semisimple groups of types B, C, and D, providing a complete description and implications for unramified cohomology of their classifying spaces.

Contribution

It offers a comprehensive determination of degree 3 invariants for these groups and shows the triviality of their unramified cohomology groups.

Findings

Complete description of degree 3 invariants for types B, C, D

Trivial unramified cohomology for classifying spaces of these groups

Advances understanding of cohomological properties of semisimple groups

Abstract

We determine the group of reductive cohomological degree $3$ invariants of all split semisimple groups of types $B$, $C$, and $D$. We also present a complete description of the cohomological invariants. As an application, we show that the group of degree $3$ unramified cohomology of the classifying space $BG$ is trivial for all split semisimple groups $G$ of types $B$, $C$, and $D$.