  We study SU(2) gluodynamics at finite temperature near the deconfining phase
transition. We create the lattice ensembles using the tadpole improved
Luscher-Weisz action. The overlap Dirac operator is used to determine the
following three aspects of vacuum structure: (i) The topological susceptibility
is evaluated at various temperatures across the phase transition, (ii) the
overlap fermion spectral density is determined and found to depend on the
Polyakov loop above the phase transition and (iii) the corresponding
localization properties of low lying eigenmodes are investigated.
