  Massless excitations at the surface of three-dimensional time-reversal
invariant topological insulators possess both fermionic and bosonic
descriptions, originating from band theory and hydrodynamic BF gauge theory,
respectively. We analyze the corresponding field theories of the Dirac fermion
and compactified boson and compute their partition functions on the
three-dimensional torus geometry. We then find some non-dynamic exact
properties of bosonization in (2+1) dimensions, regarding fermion parity and
spin sectors. Using these results, we extend the Fu-Kane-Mele stability
argument to fractional topological insulators in three dimensions.
