Bosonic Topological Insulators and Paramagnets: a view from cobordisms

TL;DR

This paper classifies bosonic topological phases in up to four spatial dimensions using cobordism theory, revealing unique phases beyond traditional group cohomology classifications, including a 3D bosonic topological insulator and a 4D phase.

Contribution

It introduces a cobordism-based classification framework for bosonic topological insulators and paramagnets, identifying phases beyond group cohomology in three and four dimensions.

Findings

Confirmation of the unique 3D bosonic topological insulator with all-fermion surface states.

Identification of a single 'beyond group cohomology' phase in 4D protected by gravitational anomalies.

Classification of phases in D<4 and D=4 dimensions using cobordism methods.

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.