  The symmetry and topology of the coincidence structure, i.e. the locus of
points in configuration space corresponding to particles in the same position,
plays a critical role in extracting universal properties for few-body models
with hard-core interactions. The coincidence structure is a scale-invariant
union of manifolds possessing rich symmetry. When there are zero-range
hard-core two-body interactions, the coincidence structure forms a nodal
surface for finite-energy wave functions in configuration space. More
generally, it acts like a defect that changes the topology of configuration
space in a way that depends on the dimension of the underlying space, the total
number of particles, and the number of particles in the hard-core interaction.
We show that for the specific case of three-body hard-core interactions in
one-dimension, the configuration space is no longer simply-connected, providing
a topological explanation for several models that exhibit anyonic behavior.
