Tagged Questions

35
votes
8answers
3k views

Questions about analogy between Spec Z and 3-manifolds

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 …
10
votes
0answers
577 views

Is there an “arithmetic cobordism category”?

This question is a clumsy attempt to apply a certain analogy. I hope that if the answer is negative it comes with a clarification of the scope and limitations of the analogy. Ari …
7
votes
2answers
890 views

Spec Z analogue of Thurston program?

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 …
5
votes
2answers
424 views

Zeta function for curves in a manifold

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 …