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A correspondence between distances and embeddings for manifolds: New techniques for applications of the Abstract Boundary

Whale, Benjamin; Scott, Susan M


We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the 'edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Journal of Geometry and Physics
DOI: 10.1016/j.geomphys.2010.12.013


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