Real Algebraic and Analytic Geometry
Submission: 2011, December 2.
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 (2010): 0364, 22F99.
Full text: http://arxiv.org/pdf/1106.3442