  We present a phase diagram study of the O(4) model as an effective theory for
2-flavor QCD. In the chiral limit, both theories perform spontaneous symmetry
breaking with isomorphic groups, which suggests that they belong to the same
universality class. Since we are interested in high temperature, we further
assume dimensional reduction to the 3d O(4) model, which implies topological
sectors. According to Skyrme and others, the corresponding topological charge
represents the baryon number. Hence the baryon chemical potential $\mu_{B}$
appears as an imaginary vacuum angle, which can be included in the lattice
simulations without any sign problem. We present simulation results for the
critical line in the chiral limit, and for the crossover in the presence of
light quark masses. The shapes of these lines are compatible with other
conjectures, but up to about $\mu_{B} \approx 300$ MeV we do not find a
Critical Endpoint, although there are indications for it to be near-by.
