  Using the geometric definition of the topological charge we decompose the
path integral of 2-dimensional U(1) lattice gauge theory into topological
sectors. In a Monte Carlo simulation we compute the average value of the action
as well as the distribution of its values for each sector separately. These
numbers are compared with analytic lower bounds of the action which are
relevant for classical configurations carrying topological charge. We find that
quantum fluctuations entirely dominate the path integral. Our results for the
probability distribution of the Monte Carlo generated configurations among the
topological sectors can be understood by a semi-phenomenological argument.
