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Arithmetic topology of 4-manifolds

Geometric Topology 2021-08-12 v4 Algebraic Topology Number Theory

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.

Keywords

Cite

@article{arxiv.1907.03901,
  title  = {Arithmetic topology of 4-manifolds},
  author = {Igor Nikolaev},
  journal= {arXiv preprint arXiv:1907.03901},
  year   = {2021}
}

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10 pages, an update