Real Algebraic and Analytic Geometry

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336. Annalisa Conversano, Anand Pillay:
Connected components of definable groups, and o-minimality II.


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.

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