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 ent
ropy 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.
