Abstract We study the non-perturbative effects of the global features of the configuration space for SU(2) gauge theory on the three-sphere. The strategy is to reduce the full problem to an effective theory for the dynamics of the low-energy modes. By explicitly integrating out the high-energy modes, the one-loop correction to the effective hamiltonian is obtained. Imposing the f dependence through boundary conditions in configuration space incorporates the non-perturbative effects of the non-contractable loops in the full configuration space. After this we obtain the glueball spectrum of the effective theory with a variational method.