I'm not sure if the questions make sense: Conc. primes as knots and Spec Z as 3-manifold - fits that to the Poincare conjecture? Topologists view 3-manifolds as Kirby-equivalence …

Motivation In the analogy between prime numbers and knots, the prime number is thought sometimes as the circle of length $l([p]) = \text{log}\,p$. This is so you can express the z …

It's been known for a while that primes in number fields can be thought of, from an algebraic point of view, to be similar to knots in 3-manifolds. A good reference (thanks to this …