  The 2+1D topological order can be characterized by the mapping-class-group
representations for Riemann surfaces of genus-1, genus-2, etc. In this paper,
we use those representations to determine the possible gapped boundaries of a
2+1D topological order, as well as the domain walls between two topological
orders. We find that mapping-class-group representations for both genus-1 and
genus-2 surfaces are needed to determine the gapped domain walls and
boundaries. Our systematic theory is based on the fixed-point partition
functions for the walls (or the boundaries), which completely characterize the
gapped domain walls (or the boundaries). The mapping-class-group
representations give rise to conditions that must be satisfied by the
fixed-point partition functions, which leads to a systematic theory. Such
conditions can be viewed as bulk topological order determining the
(non-invertible) gravitational anomaly at the domain wall, and our theory can
be viewed as finding all types of the gapped domain wall given a
(non-invertible) gravitational anomaly. We also developed a systematic theory
of gapped domain walls (boundaries) based on the structure coefficients of
condensable algebras.
