Folded and/or compacted dimensions in M-theory?
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Extra dimensions are at each point of the 4-dimensional spacetime.
The whole 10- or 11-dimensional spacetime has the shape of M^3+1 × X where XX is the 6 - or 7-dimensional manifold and the first factor is the 3+1-dimensional spacetime manifold we used to think is "everything".
It's a Cartesian product. It may also be a warped product but I don't want to go into these things.
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