On the o-minimal Hilbert's fifth problem

2015/07/13 by Mário J. Edmundo, Marcello Mamino, Edmundo, Mario J. +7
Mathematics · #03C64 #55N30 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1507.03531

openalex publication_date 2015/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbb M be an arbitrary o-minimal structure. Let G be a definably compact definably connected abelian definable group of dimension n. Here we compute the new the intrinsic o-minimal fundamental group of G; for each k>0, the k-torsion subgroups of G; the o-minimal cohomology algebra over \mathbb Q of G. As a corollary we obtain a new uniform proof of Pillay's conjecture, an o-minimal analogue of Hilbert's fifth problem, relating definably compact groups to compact real Lie groups, extending the proof already known in o-minimal expansions of ordered fields.

Citations

• On groups and fields definable in o-minimal structures
• Geometric categories and o-minimal structures

Related

• O-minimal cohomology and definably compact definable groups
• Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup
• O-minimal spectra, infinitesimal subgroups and cohomology
• Solvable groups definable in o-minimal structures
• Groups definable in weakly o-minimal non-valuational structures