  Let V_0 and V_1 be complex vector bundles over a space X. We use the theory
of divisors on formal groups to give obstructions in generalised cohomology
that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that
V_0\cap V_1 has dimension at least k everywhere. We study various algebraic
universal examples related to this question, and show that they arise from the
generalised cohomology of corresponding topological universal examples. This
extends and reinterprets earlier work on degeneracy classes in ordinary
cohomology or intersection theory.
