What Bordism-Theoretic Anomaly Cancellation Can Do for U

We perform a bordism computation to show that the E₇₍₇₎(R) E 7 ( 7 ) ( R ) U-duality symmetry of 4d N = 8 N = 8 supergravity could have an anomaly invisible to perturbative methods; then we show that this anomaly is trivial. We compute the relevant bordism group using the Adams and Atiyah–Hirzebruch spectral sequences, and we show the anomaly vanishes by computing η η -invariants on the Wu manifold, which generates the bordism group.