  We introduce topological magnetic field in two-dimensional flat space, which
admits a solution of scalar monopole that describes the nontrivial topology. In
the Chern-Simons gauge field theory of anyons, we interpret the anyons as the
quasi-particles composed of fermions and scalar monopoles in such a form that
each fermion is surrounded by infinite number of scalar monopoles. It is the
monopole charge that determines the statistics of anyons. We re-analyze the
conventional arguments of the connection between topology and statistics in
three-dimensional space, and find that those arguments are based on the global
topology, which is relatively trivial compared with the monopole structure.
Through a simple model, we formulate the three-dimensional anyon field
  using infinite number of Dirac's magnetic monopoles that change the ordinary
spacetime topology. The quasi-particle picture of the three-dimensional anyons
is quite similar to that of the usual two-dimensional anyons. However, the
exotic statistics there is not restricted to the usual fractional statistics,
but a functional statistics.
