  We propose a correspondence between topological order in 2+1d and Seifert
three-manifolds together with a choice of ADE gauge group $G$. Topological
order in 2+1d is known to be characterized in terms of modular tensor
categories (MTCs), and we thus propose a relation between MTCs and Seifert
three-manifolds. The correspondence defines for every Seifert manifold and
choice of $G$ a fusion category, which we conjecture to be modular whenever the
Seifert manifold has trivial first homology group with coefficients in the
center of $G$. The construction determines the spins of anyons and their
S-matrix, and provides a constructive way to determine the R- and F-symbols
from simple building blocks. We explore the possibility that this
correspondence provides an alternative classification of MTCs, which is put to
the test by realizing all MTCs (unitary or non-unitary) with rank $r\leq 5$ in
terms of Seifert manifolds and a choice of Lie group $G$.
