  Canonical quantization of abelian BF-type topological field theory coupled to
extended sources on generic d-dimensional manifolds and with curved line
bundles is studied. Sheaf cohomology is used to construct the appropriate
topological extension of the action and the topological flux quantization
conditions, in terms of the Cech cohomology of the underlying spatial manifold,
as required for topological invariance of the quantum field theory. The
wavefunctions are found in the Hamiltonian formalism and are shown to carry
multi-dimensional representations of various topological groups of the space.
Expressions for generalized linking numbers in any dimension are thereby
derived. In particular, new global aspects of motion group presentations are
obtained in any dimension. Applications to quantum exchange statistics of
objects in various dimensionalities are also discussed.
