A sense of how manifolds are applied in practice may be gleaned from the set of excerpts linked below, from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, which I used in discussing differentiable manifolds with other participants in the IEEE Standard Upper Ontology Working Group.
What brought the concept of a manifold to mind in that context was a set of problems associated with perspectivity, relativity, and interoperability among multiple ontologies. To my way of thinking, those are the very sorts of problems manifolds were invented to handle.
Reference
- Doolin, Brian F., and Martin, Clyde F. (1990), Introduction to Differential Geometry for Engineers, Marcel Dekker, New York, NY.
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