play an important part in many quantum field theories. This is especially true of gauge theories. There are also [*topological quantum field theories*]{} in which the excitations are purely topological and the classical phase spaces of these theories usually reduce to a finite dimensional space: these spaces can be zero dimensional discrete sets, or whole moduli spaces. The semi-classical, or stationary phase, approximation to the functional integral of such a theory is then a weighted sum, or integral, over the [*finite dimensional*]{} phase space. In addition, for some of these theories, this approximation is [*exact*]{} providing thereby a reduction of the functional integral to a finite dimensional integral.

If a topological quantum field theory contains a gauge field the reduced functional integral mentioned above often consists of sums or integrals over [*flat*]{} connections; the non-triviality of such connections is determined purely by their holonomy, and, if $A$ is a flat connection over a manifold $M$, its holonomy is an element of the fundamental group $\pi_1(M)$. This means that an ideal laboratory within which to study such theories is provided by taking the manifold $M$ to have a non-trivial fundamental group but to be otherwise topologically rather simple. An ideal way 