Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.minimal surfaces | topological transitions | systoles T he study of singularities, be it their dynamic evolution (1-3) or their location and structure in a system at equilibrium (4, 5), has a long history. The main focus of research has been either on systems without boundaries, where both the static and dynamic cases are fairly well understood, or on finite systems with prescribed boundaries displaying static singularities, as for example defects in liquid crystals (6) and superfluids (7), Langmuir monolayers (8), and quantum field theories (9). Work on dynamic aspects of these bounded systems is limited, particularly in the case of singularity formation accompanying a topological change (10). For instance, to our knowledge, there is no mathematical tool available to predict from initial conditions whether a singularity in a bounded system will occur in the bulk or at the boundary.In a previous paper (11) we found that a soap film in the shape of a Möbius band spanning a slowly deforming wire would change its topology through a singularity that occurs at the boundary. This simple example provided a first model to investigate the dynamical aspects of the formation of a boundary singularity from the moment the system becomes unstable, and until a new stable configuration is reached. While progress was made in the particular case of the Möbius band, left unanswered were questions of greater generality: (i) Are there any other configurations of films spanning...