  It is generally assumed that the gravitational field is bosonic. Here we show
that a simple propagating torsional theory can give rise to localized geometric
structures that can consistently be quantized as fermions under exchange. To
demonstrate this, we show that the model can be formally mapped onto the Skyrme
model of baryons, and we use well-known results from Skyrme theory. This begs
the question: {\it Is geometry bosonic or fermionic (or both)?}
