  Representing 3D surfaces as level sets of continuous functions over
$\mathbb{R}^3$ is the common denominator of neural implicit representations,
which recently enabled remarkable progress in geometric deep learning and
computer vision tasks. In order to represent 3D motion within this framework,
it is often assumed (either explicitly or implicitly) that the transformations
which a surface may undergo are homeomorphic: this is not necessarily true, for
instance, in the case of fluid dynamics. In order to represent more general
classes of deformations, we propose to apply this theoretical framework as
regularizers for the optimization of simple 4D implicit functions (such as
signed distance fields). We show that our representation is capable of
capturing both homeomorphic and topology-changing deformations, while also
defining correspondences over the continuously-reconstructed surfaces.
