Right, it's boring and routine maths, but there's no evidence that sort of mathematics will somehow bypass the rest of mathematics and physics. It's like suggesting that long division might solve quantum non-locality.
Or it could all match up - aren't several dimensions the very core of e.g. field theory? No idea, really, as you can tell I'm not an expert, just throwing around random words in a thread that is ultimately based on a SF story.
Yes it is, like I said it's very well known and understood. It's not a wild poorly understood frontier full of unimaginable possibilities. The actual maths of n-dimensional geometry is dull as ditchwater. There's no magic lurking there.