Localization of scalar and fermionic eigenmodes and confinement

We discuss the localization of eigenmodes of the covariant lattice Laplacian and overlap Dirac operator in lattice SU(2) gluodynamics. It occurs that the localization properties of the eigenmodes for fundamental scalars and fermions are different in confining configurations and in those from which confining disorder was eliminated by center-vortex removal. Localization of eigenmodes on subspaces of dimension less than four indicates the existence of the low dimensional structures in the confining vacuum.