This is a good short story (no suprise there), but unlike most Alastair Reynold's stories it is set on Earth, admitted a future Earth. The population of Earth (expect a few thousand) is cryogenically frozen for reason that are explain but it would be a spoiler to explain why here. One of the first to be frozen, a former CEO of an AI company, is selected to be revived for caretaker duties on what sounds like oil-rig-like structures where the whole of human race is being stored.
Creatures of the deep, AI emergence and other dimensions all play a role - so you won't miss out on the elements of Reynold's other books.
Confession time - when I first download this onto the Kindle I wasn't aware it was short story/novella in an anthology Apocalyptic SF by Mike Ashley, I thought it was a short story by Alastair Reynolds. I enjoyed it so much I download the anthology.
Other reviews can be found at: http://bestsf.net/alastair-reynolds-sleepover-the-mammoth-book-of-apocalyptic-sf/
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