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Cusp transitivity in hyperbolic 3-manifolds

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Abstract

In this paper, we study multiply transitive actions of the group of isometries of a cusped finite-volume hyperbolic 3-manifold on the set of its cusps. In particular, we prove a conjecture of Vogeler that there is a largest integer k for which such k-transitive actions exist, and that for each integer \(k \ge 3\), there is an upper bound on the possible number of cusps.

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Acknowledgements

We thank Matthias Goerner for providing us with graphic files for Figs. 1, 4, and 5, that first appeared in [1], and for helpful communications concerning his hyperbolic 3-manifold odode02_00912.

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  1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    John G. Ratcliffe & Steven T. Tschantz

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  1. John G. Ratcliffe
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  2. Steven T. Tschantz
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Correspondence to John G. Ratcliffe.

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Ratcliffe, J.G., Tschantz, S.T. Cusp transitivity in hyperbolic 3-manifolds. Geom Dedicata 212, 141–152 (2021). https://doi.org/10.1007/s10711-020-00552-4

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  • DOI: https://doi.org/10.1007/s10711-020-00552-4

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