Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

Understand

We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G.

• This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification.
• We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in various dimensions.