Submission date: 13 July 2015.

Abstract:

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

Keywords and phrases:

Full text arXiv 1507.03531: pdf, ps.