Backfiring Bosonisation in Diverse Dimensions

Summing over spin structures in quantum field theory can be obstructed by a mod-16 anomaly extending the familiar fermion-parity anomaly. This talk uses homotopy theory and cobordism-group cohomology to explain the obstruction, its consequences for operations such as the GSO projection and dualities, and extensions involving other dimensions, symmetries and symmetry topological field theories.