  We show that the edge states of the four-dimensional class A system can have
topological charges, which are characterized by Abelian/non-Abelian monopoles.
The edge topological charges are a new feature of relations among theories with
different dimensions. From this novel viewpoint, we provide a non-Abelian
analogue of the TKNN number as an edge topological charge, which is defined by
an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm
construction. Furthermore, putting a constant magnetic field yields an edge
monopole in a non-commutative momentum space, where D-brane methods in string
theory facilitate study of edge fermions.
