  We show how changes in unitarity-preserving boundary conditions allow
continuous interpolation among the Hilbert spaces of quantum mechanics on
topologically distinct manifolds. We present several examples, including a
computation of entanglement entropy production. We discuss approximate
realization of boundary conditions through appropriate interactions, thus
suggesting a route to possible experimental realization. We give a theoretical
application to quantization of singular Hamiltonians, and give tangible form to
the "many worlds" interpretation of wave functions.
