  In the standard $R^4$ embedding of the chiral O(4) model in 3+1 dimensions
the winding number is not conserved near the chiral phase transition and thus
no longer can be identified with baryon number. In order to reestablish
conserved baryon number in effective low-energy models near and above the
critical temperature $T_c$ it is argued that insisting in O(N) models on the
angular nature of the chiral fields with fixed boundary conditions restores
conservation of winding number. For N=2 in 1+1 dimensions it is illustrated
that as a consequence of the angular boundary conditions nontrivial solutions
exist which would be unstable in $R^2$; moving trajectories avoid crossing the
origin; and time evolution of random configurations after a quench leads to
quasistable soliton-antisoliton ensembles with net winding number fixed.
