Submission date: 30 January 2019

Abstract:

We show that for G a simple compact Lie group, the infinitesimal subgroup G^{00} is bi-intepretable with a real closed valued field. We deduce that for G an infinite definably compact group definable in an o-minimal expansion of a field, G^{00} is bi-interpretable with the disjoint union of a (possibly trivial) ℚ-vector space and finitely many (possibly zero) real closed valued fields.

Mathematics Subject Classification: 03C64, 22E15

Keywords and phrases:

Full text arXiv 1901.10831: pdf, ps.