  Quantum Gravity admits topological excitations of microscopic scale which can
manifest themselves as particles --- topological geons. Non-trivial spatial
topology also brings into the theory free parameters analogous to the
$\theta$-angle of QCD. We show that these parameters can be interpreted in
terms of geon properties. We also find that, for certain values of the
parameters, the geons exhibit new patterns of particle identity together with
new types of statistics. Geon indistinguishability in such a case is expressed
by a proper subgroup of the permutation group and geon statistics by a
(possibly projective) representation of the subgroup.
