Freedman, Michael H.; Kitaev, Alexei; Lurie, Jacob Diameters of homogeneous spaces. (English) Zbl 1029.22031 Math. Res. Lett. 10, No. 1, 11-20 (2003). Motivated by some questions from quantum computing, the authors consider the following question: Given a compact connected Lie group \(G\) with trivial center and a closed subgroup \(H\) of \(G\), how small can the homogeneous space \(G/H\) get without being trivial. They show that if one equips \(G\) with the metric derived from the operator norm of the adjoint representation, then the diameter of \(G/H\) with respect to the induced metric is bounded below by a constant which is roughly 0.12. The proof depends on a result which says that elements of discrete subgroups which are small in norm have to commute. Reviewer: Joachim Hilgert (Clausthal) Cited in 3 Documents MSC: 22F30 Homogeneous spaces 53C30 Differential geometry of homogeneous manifolds 22C05 Compact groups 22E46 Semisimple Lie groups and their representations Keywords:compact groups; operator norm; discrete subgroups PDFBibTeX XMLCite \textit{M. H. Freedman} et al., Math. Res. Lett. 10, No. 1, 11--20 (2003; Zbl 1029.22031) Full Text: DOI arXiv