  A 2+1-dimensional topological quantum field theory (TQFT) may or may not
admit topological (gapped) boundary conditions. A famous necessary, but not
sufficient, condition for the existence of a topological boundary condition is
that the chiral central charge $c_-$ has to vanish. In this paper, we consider
conditions associated with "higher" central charges, which have been introduced
recently in the math literature. In terms of these new obstructions, we
identify necessary and sufficient conditions for the existence of a topological
boundary in the case of bosonic, Abelian TQFTs, providing an alternative to the
identification of a Lagrangian subgroup. Our proof relies on general aspects of
gauging generalized global symmetries. For non-Abelian TQFTs, we give a
geometric way of studying topological boundary conditions, and explain certain
necessary conditions given again in terms of the higher central charges. Along
the way, we find a curious duality in the partition functions of Abelian TQFTs,
which begs for an explanation via the 3d-3d correspondence.
