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Diameter of homogeneous spaces: an effective account

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Abstract

In this paper we prove explicit estimates for the size of small lifts of points in homogeneous spaces. Our estimates are polynomially effective in the volume of the space and the injectivity radius.

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Notes

  1. The discussion in [11, §5.9] assumes that \({\tilde{\textbf{L}}}\) is \(\mathbb {Q}\)-almost simple; since \({\tilde{\textbf{L}}}\) is simply connected and semisimple, we can decompose \({\tilde{\textbf{L}}}={\tilde{\textbf{L}}}_1\cdots {\tilde{\textbf{L}}}_r\) as a direct product of \(\mathbb {Q}\)-almost simple factors and apply the argument to each factor separately.

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Acknowledgements

A.M. acknowledges support from the NSF and Alfred P. Sloan Research Fellowship.

A.S-G. acknowledges support from the NSF (Grant no. 1602137) and Alfred P. Sloan Research Fellowship.

F.T. acknowledges support from the Fonds National de la Recherche, Luxembourg (Grant no. 11275005).

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Correspondence to A. Mohammadi.

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Communicated by Andreas Thom.

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Mohammadi, A., Golsefidy, A.S. & Thilmany, F. Diameter of homogeneous spaces: an effective account. Math. Ann. 385, 1–40 (2023). https://doi.org/10.1007/s00208-022-02389-6

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  • DOI: https://doi.org/10.1007/s00208-022-02389-6

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