  We study a correspondence between spin three-manifolds and bosonic abelian
topological orders. Let $N$ be a spin three-manifold. We can define a
$(2+1)$-dimensional topological order $\mathrm{TO}_N$ as follows: its anyons
are the torsion elements in $H_1(N)$, the braiding of anyons is given by the
linking form, and their topological spins are given by the quadratic refinement
of the linking form obtained from the spin structure. Under this
correspondence, a surgery presentation of $N$ gives rise to a classical
Chern--Simons description of the associated topological order $\mathrm{TO}_N$.
We then extend the correspondence to spin bordisms between three-manifolds, and
domain walls between topological orders. In particular, we construct a domain
wall $\mathcal{D}_M$ between $\mathrm{TO}_N$ and $\mathrm{TO}_{N'}$, where $M$
is a spin bordism from $N$ to $N'$. This domain wall unfolds to a composition
of a gapped boundary, obtained from anyon condensation, and a gapless Narain
boundary CFT.
