The story starts with a Neanderthal being dumped from their world's Sudbury Nickel Mine into ours, via a quantum computer. On our side, he has to be saved from the heavy water he landed in, kept from the raging government, and then quarantined. On their side, because of their society and computing advances, they assume his partner killed him, and the partner is accused of murder, the punishment for which is not death, but sterilization for him and everybody who shares his genes.
The Neaderthal society is rather socialized and doesn't make a lot of sense. As usual, the author has left no space for people like me (maybe they kill disabled people, but it doesn't say what they do). We learn a lot about Neanderthal men, but not Neanderthal women, and in our world, there is an unnecessary rape scene to cause sympathy.
The Neanderthal emotions and such are close enough to ours to recognize, which also seems kind of unlikely. In some places, Sawyer has put invented words in the book, but in others, he just uses ours and there seems to be no particular reason. A tabant in their world is clearly a guardian in our world. And the technology they have that we don't doesn't have invented words.
We all agreed that the basic story was pretty good, but the worldbuilding and physics were unbelievable. If you like Sawyer, you've probably already read this. If you don't like Sawyer, don't bother with this.