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Remark on Arithmetic Topology by Nikolaev, Igor is a scholarly article available to read on EtoBox.

What is Remark on Arithmetic Topology about?

We formalize the arithmetic topology, i.e. a relationship between knots and primes. Namely, using the notion of a cluster C*-algebra we construct a functor from the category of 3-dimensional manifolds M to a category of algebraic number fields K, such that the prime ideals (ideals, resp.) in the ring of integers of K correspond to knots (links, resp.) in M. It is proved that the functor realizes all axioms of the arithmetic topology conjectured in the 1960's by Manin, Mazur and Mumford.

Author

Nikolaev, Igor

Published

2017

Language

EN