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G-linear sets and torsion points in definably compact groups

Margarita Otero & Ya’Acov Peterzil

Archive for Mathematical Logic 48 (5):387-402 (2009)

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Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup.Alessandro Berarducci - 2009 - Journal of Symbolic Logic 74 (3):891-900.details By recent work on some conjectures of Pillay, each definably compact group in a saturated o-minimal structure is an extension of a compact Lie group by a torsion free normal divisible subgroup, called its infinitesimal subgroup. We show that the infinitesimal subgroup is cohomologically acyclic. This implies that the functorial correspondence between definably compact groups and Lie groups preserves the cohomology. Download Export citation Bookmark 1 citation
Locally definable homotopy.Elías Baro & Margarita Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.details In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...) Download Export citation Bookmark 4 citations
Locally definable homotopy.Elías Baro & Marg\ Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.details In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...) Download Export citation Bookmark 4 citations

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