Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778605 | Advances in Mathematics | 2017 | 53 Pages |
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: (i) the new intrinsic o-minimal fundamental group of G; (ii) for each k>0, the k-torsion subgroups of G; (iii) 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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mário J. Edmundo, Marcello Mamino, Luca Prelli, Janak Ramakrishnan, Giuseppina Terzo,