What Bordism-Theoretic Anomaly Cancellation Can Do for U

We perform a bordism computation to show that the E₇₍₇₎(R) U-duality symmetry of 4d 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-invariants on the Wu manifold, which generates the bordism group.