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This article makes it clear that I'm missing a lot of math background. Anyone have a good source for getting up to speed on tensors and manifolds?

Here's a standard Topology textbook which will get you up to speed on manifolds: http://www.maths.ed.ac.uk/~aar/papers/munkres2.pdf

And here's Schroedinger's Space-Time Structure which has an intro to tensors: http://strangebeautiful.com/other-texts/schrodinger-st-struc...