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Diameters of Homogeneous Spaces

Michael Freedman·Alexei Kitaev·Jacob Lurie
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Abstract

Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |_{G} which induces a bi-invariant metric d_G(x,y)=|Ad(yx^{-1})|_{G} on G. We prove the existence of a constant β\approx .12 (independent of G) such that for any closed subgroup H \subsetneq G, the diameter of the quotient G/H (in the induced metric) is \geq β.

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Michael Freedman, Alexei Kitaev, Jacob Lurie. 2002-12-04. Diameters of Homogeneous Spaces. https://arxiv.org/abs/quant-ph/0209113

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