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Preprint Number 890
890. Mario J. Edmundo, Marcello Mamino, Luca Prelli, Janak Ramakrishnan and Giuseppina Terzo
On the o-minimal Hilbert's fifth problem
Submission date: 13 July 2015.
Let 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 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.
Mathematics Subject Classification: 03C64, 55N30
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