Decomposing non-manifold objects in arbitrary dimensions

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We address the problem of building valid representations of non-manifold d-dimensional objects through an approach based on decomposing a non-manifold d-dimensional object into an assembly of more regular components. We first define a standard decomposition of d-dimensional non-manifold objects described by abstract simplicial complexes. This decomposition splits a non-manifold object into components that belong to a well-understood class of objects, that we call initial quasi-manifold. Initial quasi-manifolds cannot be decomposed without cutting them along manifold faces. They form a decidable superset of d-manifolds for d⩾3, and coincide with manifolds for d⩽2. We then present an algorithm that computes the standard decomposition of a general non-manifold complex. This decomposition is unique, and removes all singularities which can be removed without cutting the complex along its manifold faces.