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Results tagged with arithmetic-topology
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user 65
Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds.
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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 question) would be …
- 15.1k
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Questions about analogy between Spec Z and 3-manifolds
From reading the Morishita article 0904.3399 (page 24), there is a following analogue of Poincare conjecture:
Suppose that k is a number field whose ring of integers $\mathscr O_k$ is “cohomologic …
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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 zeta function as
$$ …
- 15.1k