  Abelian topologically massive gauge theories (TMGT) provide a topological
mechanism to generate mass for any p-tensor boson in any dimension. Within the
Hamiltonian formulation, the embedded topological field theory (TFT) is not
made manifest. We therefore introduce a gauge invariant factorization of the
classical phase space in two orthogonal sectors. The first of these sectors is
that of gauge invariant dynamical variables with massive excitations. The
second is that of a decoupled TFT. Through canonical quantization, a
factorization of quantum states arises, enabling the projection from TMGT onto
topological quantum field theories in a most transparent way.
