  We discuss some of the key topological aspects of a two $(1+1)$-dimensional
(2D) self-interacting non-Abelian gauge theory (having no interaction with
matter fields) in the framework of {\it chiral} superfield formalism. We
provide the geometrical interpretation for the Lagrangian density, symmetric
energy momentum tensor, topological invariants, etc., by exploiting the {\it
on-shell} nilpotent BRST- and co-BRST symmetries that emerge after the
application of (dual) horizontality conditions. We show that the above
physically interesting quantities geometrically correspond to the translation
of some local (but composite) {\it chiral} superfields along one of the two
independent Grassmannian directions of a four ($2+2)$-dimensional
supermanifold. This translation is generated by the conserved and on-shell
nilpotent (co-)BRST charges that are present in the theory.
