  We propose a generic construction of exactly soluble \emph{local bosonic
models} that realize various topological orders with gappable boundaries. In
particular, we construct an exactly soluble bosonic model that realizes a 3+1D
$Z_2$ gauge theory with emergent fermionic Kramer doublet. We show that the
emergence of such a fermion will cause the nucleation of certain topological
excitations in space-time without pin$^+$ structure. The exactly soluble model
also leads to a statistical transmutation in 3+1D. In addition, we construct
exactly soluble bosonic models that realize 2 types of time-reversal symmetry
enriched $Z_2$-topological orders in 2+1D, and 20 types of simplest
time-reversal symmetry enriched topological (SET) orders which have only one
non-trivial point-like and string-like topological excitations. Many physical
properties of those topological states are calculated using the exactly soluble
models. We find that some time-reversal SET orders have point-like excitations
that carry Kramer doublet -- a fractionalized time-reversal symmetry. We also
find that some $Z_2$ SET orders have string-like excitations that carry
anomalous (non-on-site) $Z_2$ symmetry, which can be viewed as a
fractionalization of $Z_2$ symmetry on strings. Our construction is based on
cochains and cocycles in algebraic topology, which is very versatile. In
principle, it can also realize emergent topological field theory beyond the
twisted gauge theory.
