Connected components of definable groups, and o-minimality II

2011/06/17 by Annalisa Conversano, Anand Pillay, Conversano, Annalisa +1 · 1 citation
Mathematics · #0364 #22F99 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO #msc:0364 #msc:22F99

paper · pdf · doi:10.48550/arxiv.1106.3442

22 pages

arxiv created 2011/06/17 · arxiv updated 2011/06/20

Abstract

We study the connected components G⁰0, G⁰00 and their quotients for a group G definable in a saturated o-minimal expansion of a real closed field. We show that G⁰0/G⁰00 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.

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