Connected components of definable groups, and o-minimality II

Annalisa Conversano, Anand Pillay

Published 2011-06-17Version 1

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.