  In gauge theories the field configurations often occur in distinct
topological sectors. In a lattice regularised system with chiral fermions,
these sectors can be defined by referring to the Atiyah-Singer Index Theorem.
However, if such a model is simulated with local updates of the lattice gauge
configuration, the Monte Carlo history tends to get stuck in one sector for
many steps, in particular on fine lattices. Then expectation values can be
measured only within specific sectors. Here we present a pilot study in the
2-flavour Schwinger model which explores methods of approximating the complete
result for an observable - corresponding to a suitable sum over all sectors -
based on numerical measurements in a few specific topological sectors. We also
probe various procedures for an indirect evaluation of the topological
susceptibility, starting from such topologically restricted measurements.
