Consistency of M-Theory on Non-Orientable Manifolds

Abstract We prove that there is no parity anomaly in M-theory the low-energy field theory approximation. Our approach computational. determine generators for 12-dimensional bordism group of pin manifolds with a w1-twisted integer lift w4; these are on which Wick-rotated exists. The cancellation comes down to computing specific η-invariant and cubic form manifolds. Of interest beyond this problem our expositions computational techniques η-invariants, algebraic forms, Adams spectral sequence anomalies spinor fields Rarita–Schwinger fields.