Cusp transitivity in hyperbolic 3-manifolds

2019/12/09 by Ratcliffe, John G., Tschantz, Steven T.
#20B20 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1912.04192

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 k for which such k-transitive actions exist, and that for each k ≥ 3, there is an upper bound on the possible number of cusps.

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