  In a recent paper, Teo and Kane proposed a 3D model in which the defects
support Majorana fermion zero modes. They argued that exchanging and twisting
these defects would implement a set R of unitary transformations on the zero
mode Hilbert space which is a 'ghostly' recollection of the action of the braid
group on Ising anyons in 2D. In this paper, we find the group T_{2n} which
governs the statistics of these defects by analyzing the topology of the space
K_{2n} of configurations of 2n defects in a slowly spatially-varying gapped
free fermion Hamiltonian: T_{2n}\equiv {\pi_1}(K_{2n})$. We find that the group
T_{2n}= Z \times T^r_{2n}, where the 'ribbon permutation group' T^r_{2n} is a
mild enhancement of the permutation group S_{2n}: T^r_{2n} \equiv \Z_2 \times
E((Z_2)^{2n}\rtimes S_{2n}). Here, E((Z_2)^{2n}\rtimes S_{2n}) is the 'even
part' of (Z_2)^{2n} \rtimes S_{2n}, namely those elements for which the total
parity of the element in (Z_2)^{2n} added to the parity of the permutation is
even. Surprisingly, R is only a projective representation of T_{2n}, a
possibility proposed by Wilczek. Thus, Teo and Kane's defects realize
`Projective Ribbon Permutation Statistics', which we show to be consistent with
locality. We extend this phenomenon to other dimensions, co-dimensions, and
symmetry classes. Since it is an essential input for our calculation, we review
the topological classification of gapped free fermion systems and its relation
to Bott periodicity.
