  We use Floer's exact triangle to study the u-map (cup product with the
4-dimensional class) in the Floer cohomology groups of admissible SO(3) bundles
over closed, oriented 3-manifolds. In the case of non-trivial bundles we show
that (u^2-64)^n = 0 for some positive integer n. For homology 3-spheres Y the
same holds for a certain reduced Floer group, which is obtained from the
ordinary one by factoring out interaction with the trivial connection. This
leads to a new proof (in the simply-connected case) of the finite type
conjecture of Kronheimer and Mrowka concerning the structure of Donaldson
polynomials. In the case of rational coefficients, interaction with the trivial
connection is measured by a single integer h(Y), which is additive under
connected sums and depends only on the rational homology cobordism class of Y.
