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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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Lengths of tangles and prime numbers

Akshay Venkatesh recently gave a nice public lecture at the IAS on the analogy between primes and knots. The analogy involves a conversion factor, which is described in the talk as follows: given a …