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Counting Overlattices in Automorphism Groups of Trees

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Abstract

We give an upper bound for the number u Γ(n) of “overlattices” in the automorphism group of a tree, containing a fixed lattice Γ with index n. For an example of Γ in the automorphism group of a 2p-regular tree whose quotient is a loop, we obtain a lower bound of the asymptotic behavior as well.

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Authors and Affiliations

  1. Yale University, PO Box 208283, New Haven, CT, 06520-8283, U.S.A

    Seonhee Lim

  2. ENS Paris, UMR 8553, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Seonhee Lim

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  1. Seonhee Lim
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Correspondence to Seonhee Lim.

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Lim, S. Counting Overlattices in Automorphism Groups of Trees. Geom Dedicata 118, 1–21 (2006). https://doi.org/10.1007/s10711-004-4196-7

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  • DOI: https://doi.org/10.1007/s10711-004-4196-7

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