It has been known for some time that topological geons in quantum gravity m
ay lead to a complete violation of the canonical spin-statistics relation:
There may be no connection between spin and statistics for a pair of geons.
We present an algebraic description of quantum gravity in a (2 + 1)D manif
old of the form Sigma x R, based on the first-order canonical formalism of
general relativity. We identify a certain algebra describing the system, an
d obtain its irreducible representations. We then show that although the us
ual spin-statistics theorem is not valid, statistics is completely determin
ed by spin for each of these irreducible representations, provided one of t
he labels of these representations, which we call flux, is superselected. W
e argue that this is indeed the case. Hence, a new spin-statistics theorem
can be formulated.