# On gapped boundaries for SPT phases beyond group cohomology

## TL;DR

This paper introduces a generalized symmetry extension method to construct gapped boundaries for a broad class of SPT phases beyond group cohomology, including time-reversal-invariant bosonic and fermionic phases.

## Contribution

It extends the symmetry extension approach to non-cohomological SPT phases, enabling gapped boundary constructions for fermionic and time-reversal-invariant phases.

## Key findings

- Constructed gapped boundaries for time-reversal-invariant bosonic SPT phases.
- Extended the method to fermionic Gu-Wen SPT phases.
- Applicable to arbitrary finite internal symmetry groups.

## Abstract

We discuss a strategy to construct gapped boundaries for a large class of symmetry-protected topological phases (SPT phases) beyond group cohomology. This is done by a generalization of the symmetry extension method previously used for cohomological SPT phases. We find that this method allows us to construct gapped boundaries for time-reversal-invariant bosonic SPT phases and for fermionic Gu-Wen SPT phases for arbitrary finite internal symmetry groups.