  On any manifold M^n, the de Rham operator D=d+d^* (with respect to a complete
Riemannian metric), with the grading of forms by parity of degree, gives rise
by Kasparov theory to a class [D] in KO_0(M), which when M is closed maps to
the Euler characteristic chi(M) in KO_0(point) = Z. The purpose of this note is
to give a quick proof of the (perhaps unfortunate) fact that [D] is as trivial
as it could be subject to this constraint. More precisely, if M is connected,
[D] lies in the image of Z = KO_0(point) in KO_0(M) (induced by the inclusion
of a basepoint).
