The product formula for the third obstruction
Robert E. Mosher · Pacific Journal of Mathematics · 1968
Let ξ be an SO(w)-bundIe with n > 3; let p: E->B be the projection in the associated (n -l)-sphere bundle.In this note we express the third obstruction to a cross-section of p as a tertiary characteristic class and prove a product formula for the behavior of this class under Whitney sum.