Arithmetic topology of 4-manifolds

2019/07/08 by Igor Nikolaev, Nikolaev, Igor
Mathematics · #11R32 #16W20 #57N13 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1907.03901

openalex publication_date 2019/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the group ring of a finite abelian group
• Profinite mapping class groups
• K-theory of Etesi C*-algebras

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