  In this thesis I present my research on the exotic configurations of
antiferromagnetic systems characterised by a topological invariant. The
research presented outlines the construction of novel local antiferromagnetic
degrees of freedom for low dimensional antiferromagnetic lattices. This new
construction reproduces the real division algebra hierarchy satisfied by the
nonlinear sigma-model and reveals the presence of a novel local gauge field. I
have also studied elastic magnetic vesicles of spherical and toric genus in the
presence of a magnetic soliton. My studies reveal a global shrinking, with
local swellings in the regions where the soliton presents a spin-flip. The
geometrical origin of this novel phenomena led me to interpret the geometric
frustration of magnetic vesicles as the competition between the two topological
orders present. The microscopic mechanism and topological competition suggested
above go beyond the scope of this thesis, providing a microscopic explanation
for the Fermi-Bose transmutation and a way to deal with this type of exotic
physics.
