<<<There is one significant drawback that should not be understated. Algorithm design using topology manipulation can be enormously challenging to reason about. You are often taking a conceptually simple algorithm, like a nested loop or hash join, and replacing it with a much more efficient algorithm involving the non-trivial manipulation of complex high-dimensionality constraint spaces that effect the same result. Routinely reasoning about complex object relationships in greater than three dimensions, and constructing correct parallel algorithms that exploit them, becomes easier but never easy.>>>

http://www.jandrewrogers.com/2015/10/08/spacecurve/