  We propose a diagnostic tool for detecting non-trivial symmetry protected
topological (SPT) phases protected by a symmetry group $G$ in 2+1 dimensions.
Our method is based on directly studying the 1+1-dimensional anomalous edge
conformal field theory (CFT) of SPT phases. We claim that if the CFT is the
edge theory of an SPT phase, then there must be an obstruction to cutting it
open. This obstruction manifests in the in-existence of boundary states that
preserves both the conformal symmetry and the global symmetry $G$. We discuss
the relation between edgeability, the ability to find a consistent boundary
state, and gappability, the ability to gap out a CFT, in the presence of $G$.
We study several cases including time-reversal symmetric topological
insulators, $\mathbb{Z}_N$ symmetric bosonic SPTs, and $\mathbb{Z}_2 \times
\mathbb{Z}_2$ symmetric topological superconductors.
