  The confinement-deconfinement transition is discussed from topological
viewpoints. The topological change of the system is achieved by introducing the
dimensionless imaginary chemical potential ($\theta$). Then, the non-trivial
free-energy degeneracy becomes the signal of the deconfinement transition and
it can be visualized by using the map of the thermodynamic quantities to the
circle $S^1$ along $\theta$. To understand this "topological" deconfinement
transition at finite real quark chemical potential ($\mu_\mathrm{R}$), we
consider the isospin chemical potential ($\mu_\mathrm{iso}$) in the effective
model of QCD. The phase diagram at finite $\mu_\mathrm{iso}$ is identical with
that at finite $\mu_\mathrm{R}$ outside of the pion-condensed phase at least in
the large-$N_\mathrm{c}$ limit via the well-known orbifold equivalence. In the
present effective model, the topological deconfinement transition does not show
a significant dependence on $\mu_\mathrm{iso}$ and then we can expect that this
tendency also appears at small $\mu_\mathrm{R}$. Also, the chiral transition
and the topological deconfinement transition seems to be weakly correlated. If
we will access lattice QCD data for the temperature dependence of the quark
number density at finite $\mu_\mathrm{iso}$ with $\theta=\pi/3$, our surmise
can be judged.
