Bosonic Topological Insulators and Paramagnets: a view from cobordisms

Abstract

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 "beyond group cohomology" phase. It is protected by gravitational anomalies of the boundary theory and is stable without any additional symmetry.

arXiv comment18 pages, latex. v2: an error in the last section has been corrected, affecting the classification in D=4. Other results unchanged

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