  The generalized double semion (GDS) model, introduced by Freedman and
Hastings, is a lattice system similar to the toric code, with a gapped
Hamiltonian whose definition depends on a triangulation of the ambient manifold
$M$, but whose space of ground states does not depend on the triangulation, but
only on the underlying manifold. In this paper, we use topological quantum
field theory (TQFT) to investigate the low-energy limit of the GDS model. We
define and study a functorial TQFT $Z_{\mathrm{GDS}}$ in every dimension $n$
such that for every closed $(n - 1)$-manifold $M$, $Z_{\mathrm{GDS}}(M)$ is
isomorphic to the space of ground states of the GDS model on $M$; the
isomorphism can be chosen to intertwine the actions of the mapping class group
of $M$ that arise on both sides. Throughout this paper, we compare our
constructions and results with their known analogues for the toric code.
