Mamino, Marcello Splitting definably compact groups in o-minimal structures. (English) Zbl 1247.03062 J. Symb. Log. 76, No. 3, 973-986 (2011). Summary: An argument of A. Borel [Tohoku Math. J., II. Ser. 13, 216–240 (1961; Zbl 0109.26101), Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement. Cited in 2 Documents MSC: 03C64 Model theory of ordered structures; o-minimality 55S40 Sectioning fiber spaces and bundles in algebraic topology Keywords:definable groups; o-minimality; fibre bundles Citations:Zbl 0109.26101 PDF BibTeX XML Cite \textit{M. Mamino}, J. Symb. Log. 76, No. 3, 973--986 (2011; Zbl 1247.03062) Full Text: DOI arXiv OpenURL References: [1] DOI: 10.2748/tmj/1178244298 · Zbl 0109.26101 [2] DOI: 10.1007/s11856-010-0098-6 · Zbl 1213.03048 [3] DOI: 10.1093/qmath/hap011 · Zbl 1216.03051 [4] Israel Journal of Mathematics (2009) [5] Tame topology and o-minimal structures 248 (1998) [6] The structure of compact groups 25 (1998) [7] The topology of fibre bundles 14 (1951) · Zbl 0054.07103 [8] DOI: 10.1112/S0024610799007528 · Zbl 0935.03047 [9] DOI: 10.1016/0022-4049(88)90125-9 · Zbl 0662.03025 [10] Model theory with applications to algebra and analysis, Vol. 2 350 pp 177– (2008) [11] DOI: 10.2140/pjm.1992.154.331 · Zbl 0723.14042 [12] DOI: 10.1016/0022-4049(94)90127-9 · Zbl 0815.03024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.