Brilliant. Hard SF at its absolute best.
It's almost impossible to imagine a galaxy-spanning civilization in a universe still bounded by the absolute limitation of the speed of light, but Egan manages to do it, and do it well. Yet, the galactic civilization is almost a throwaway in this tale. The true story is about a microcosmic society in a hidden backwater.
The people of the Splinter (from the start, clearly recognizable as some kind of orbital habitat) are clearly post-apocalyptic, their science has fallen into disuse (to the degree that people know what multiplication is, but rarely learn it), and yet, faced with a threat to their future, they develop a knowledge of celestial mechanics, from Newton to Einstein, in less than a generation. That might seem hard to believe, but Egan makes it all perfectly reasonable - after all, a spinning, orbiting, object is a continually (measurably) accelerating frame of reference. Newton might have worked out Einstein's theories in such a place.
I have a background in mathematics, but my geometry is weak (I can work out geometry all the way up to 2 dimensions), and this was heavy on 4 dimensional geometry, so very hard work to keep track of. I always felt I almost
understood it all, but it was absolutely worth the effort.