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

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.