  We study a generalization of the group of loops based on sets of signed
points, instead of paths or loops. This geometrical setting incorporates the
kinematical constraints of the Sigma Model, inasmuch as the the group of loops
does with the Bianchi identities of Yang-Mills theories. We employ an Abelian
version of this construction to quantize the Self-Dual Model, which allows us
to relate this theory with that of a massless scalar field obeying non-trivial
boundary conditions.
