Looking for Effects of Topology in the Dirac Spectrum of Staggered Fermions

We classify SU(3) gauge field configurations in different topological sectors by the smearing technique. In each sector we compute the distribution of low lying eigenvalues of the staggered Dirac operator. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero. The smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are thus insensitive to gauge field topology. On the smeared configurations, $4\nu$ eigenvalues go to zero in agreement with the index theorem.