Submission date: 17 June 2011.

Abstract:

We study the connected components G^00, G^000 and their quotients for a group G definable in a saturated o-minimal expansion of a real closed field. We show that G^00/G^000 is naturally the quotient of a connected compact commutative Lie group by a dense finitely generated subgroup. We also highlight the role of universal covers of semisimple Lie groups.

Mathematics Subject Classification: 0364, 22F99

Keywords and phrases:

Full text arXiv 1106.3442: pdf, ps.