Overlap fermion with the topology conserving gauge action

We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator, $H_W$, with the gauge action whose form is designed to avoid topology change, as well as with the standard plaquette action. On the quenched lattices, the former gauge action exhibits less density of low-lying eigenmodes of $H_W$ compared to the latter at the same lattice spacing. We also show preliminary results for the dynamical simulation with two flavors of overlap fermions.