On the o-minimal Hilbert's fifth problem

Mario J. Edmundo; Marcello Mamino; Luca Prelli; Janak Ramakrishnan; Giuseppina Terzo

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arXiv · 1507.03531

On the o-minimal Hilbert's fifth problem

Mario J. Edmundo·Marcello Mamino·Luca Prelli·Janak Ramakrishnan·Giuseppina Terzo

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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.

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BibTeX RIS

Mario J. Edmundo, Marcello Mamino, Luca Prelli, Janak Ramakrishnan, Giuseppina Terzo. 2015-07-13. On the o-minimal Hilbert's fifth problem. https://arxiv.org/abs/1507.03531

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