  In QCD the gauge-invariant gluon polarization Delta G in a nucleon can be
defined either in a non-local way as the integral over the Ioffe-time
distribution of polarized gluons, or in light-cone gauge as the forward matrix
element of the local topological current. We have investigated both
possibilities within the framework of QCD sum rules. Although the topological
current is built from local fields, we have found that its matrix element
retains sensitivity to large longitudinal distances. Because QCD sum rules
produce artificial oscillations of the Ioffe-time distribution of polarized
glue at moderate and large light-like distances, the calculation of the matrix
element of the topological current results in a small value of Delta G(mu^2 = 1
GeV^2) = 0.6 \pm 0.2. In a more consistent approach QCD sum rules are used to
describe the polarized gluon distribution only at small light-like distances.
Assuming that significant contributions to Delta G arise only from longitudinal
length scales not larger than the nucleon size leads to Delta G(mu^2 = 1 GeV^2)
= 2 \pm 1.
