  Local topological charge structure in the 2D CP(N-1) sigma models is studied
using the overlap Dirac operator. Long-range coherence of topological charge
along locally 1D regions in 2D space-time is observed. We discuss the
connection between these results and the recent discovery of coherent 3D sheets
of topological charge in 4D QCD. In both cases, coherent regions of topological
charge form along surfaces of approximmate codimension 1.
