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}
}
Comments
10 pages, an update