Representation of non-manifold objects

In our previous work [2], we have shown that a non-manifold, mixed-dimensional object described by simplicial complexes can be decomposed in a unique way into regular components, all belonging to a well-understood class. Based on such decomposition, we define here a two-level topological data structure for representing non-manifold objects in any dimension: the first level represents components; while the second level represents the connectivity relation among them. The resulting data structure is compact and scalable, allowing for the efficient treatment of singularities without burdening well-behaved parts of a complex with excessive space overheads.