Bosonic Topological Insulators and Paramagnets: a view from cobordisms

Understand

We classify Bosonic Topological Insulators and Paramagnets in D<=4 spatial dimensions using the cobordism approach.

• For D<4 we confirm that the only such phase which does not fit into the group cohomology classification is the 3D Bosonic Topological Insulator protected by time-reversal symmetry whose surface admits an all-fermion topologically ordered state.
• For D=4 there is a unique &#34;beyond group cohomology&#34; phase.
• It is protected by gravitational anomalies of the boundary theory and is stable without any additional symmetry.