Arithmetic topology

Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It developed from a series of analogies between number fields and 3-manifolds; primes and knots pointed out by Barry Mazur^[1] and by Yuri Manin in the 1960s. In the 1990s Reznikov^[2] and Kapranov^[3] began studying these analogies and coined the term arithmetic topology.

Notes

^ B. Mazur, Notes on ´etale cohomology of number fields, Ann. scient. ´Ec. Norm. Sup. 6 (1973), 521-552.
^ A. Reznikov, Three-manifolds class field theory (Homology of coverings for a nonvirtually b1-positive manifold), Sel. math. New ser. 3, (1997), 361–399.
^ M. Kapranov, Analogies between the Langlands correspondence and topological quantum field theory, Progress in Math., 131, Birkhäuser, (1995), 119–151.

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v t e Number theory
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