Quantum vortex configurations in three dimensions

We examine the kinematics of quantum vortex configurations in three-dimensional space for an ideal incompressible fluid. The permitted quantum configurations are shown to be {ital surfaces} of vorticity, characterized topologically not only by their knottedness, but also by additional global properties such as twists and holes. Our results, obtained by representing an infinite-dimensional group of diffeomorphisms, contradict conclusions reached by approximating the infinite-dimensional system with finitely many degrees of freedom.