Classification of fermionic symmetry-protected topological phases

We give a systematic construction and classification of fermionic symmetry-protected topological states for generic fermionic symmetry group G_f, which is a central extension of bosonic symmetry group G_b (may contain time reversal symmetry) by the fermion parity symmetry group Z_2^f. For each class in the classification (except those with 2D p+ip chiral superconductor decorations), we construct a fixed-point wave function which admits exactly solvable commuting-projector Hamiltonian. The classification is based on the notion of equivalence class of fermionic symmetric local unitary transformations.