  The standard topological approach to indistinguishable particles formulates
exchange statistics by using the fundamental group to analyze the connectedness
of the configuration space. Although successful in two and more dimensions,
this approach gives only trivial or near trivial exchange statistics in one
dimension because two-body coincidences are excluded from configuration space.
Instead, we include these path-ambiguous singular points and consider
configuration space as an orbifold. This orbifold topological approach allows
unified analysis of exchange statistics in any dimension and predicts novel
possibilities for anyons in one-dimensional systems, including non-abelian
anyons obeying alternate strand groups. These results clarify the
non-topological origin of fractional statistics in one-dimensional anyon
models.
