Arithmetic topology of 4-manifolds

Published 8 Jul 2019 in math.GT, math.AT, and math.NT | (1907.03901v4)

Abstract: We construct a functor from the smooth 4-dimensional manifolds to the hyper-algebraic number fields, i.e. fields with non-commutative multiplication. It is proved that that the simply connected 4-manifolds correspond to the abelian extensions. We recover the Rokhlin and Donaldson's Theorems from the Galois theory of the non-commutative fields.

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Authors (1)

Igor Nikolaev

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