The last book I finished was Charlie Stross’s The Family Trade. Spoilers:
The premise: In a parallel timeline, there arises a clan with the recessive hereditary ability to jump between that world and this. The talent is triggered when the eye traces a symbol reminiscent of Celtic knotwork, so each member of the Clan carries a locket or a tattoo.
Circa 1969 a high-ranking woman of the Clan was attacked and mortally wounded, but escaped to our world with her baby daughter. The baby was adopted by a secular Jewish couple in Boston; went through med school but decided it wasn’t for her; became a tech journalist (not unlike the author, who was a pharmacist and later a tech journalist before turning to fiction). When she’s 32 years old her adoptive mother gives her a shoebox of her birth mother’s meager effects, including the trigger locket. The Clan becomes aware of her, and her uncle explains things.
At this point I wait in vain for the heroine to ask: are there only two worlds? Well, at the end of this book she kills an assassin who wears a locket with a similar but different knot, which would take her to yet another world.
I’m hoping that in the next volume she’ll find time to take the two lockets to a knot theorist at MIT and ask: what do these two figures have in common, and what other figures can you generate with the same property?
Minor spoilers.
I’ve read book 2 (The Hidden Family) and the draft for book 3.
No knot theorists are consulted.
I sent Charlie email about this.
He wrote “wait for book 4”.
So there.
On second thought, not a knot theorist: the over-under crossings are likely much less relevant than the path in the other two dimensions.
But somewhere in the second book the over-under is said to make a difference, if memory serves.