English

Volumes of ideal hyperbolic drums

Geometric Topology 2026-02-27 v1

Abstract

Milnor computed the volumes of ideal hyperbolic prisms as part of an effort to construct 3-manifolds whose volumes are finite rational sums of the Lobachevsky function evaluated at rational multiples of pi. Motivated by these results and with an eye to related applications, we prove a volume formula for arbitrary ideal hyperbolic antiprisms, also called drums.

Keywords

Cite

@article{arxiv.2602.22389,
  title  = {Volumes of ideal hyperbolic drums},
  author = {Eric Chesebro and Justin Lanier and Emma N. McQuire and James Morgan and Jessica S. Purcell and Henry Segerman},
  journal= {arXiv preprint arXiv:2602.22389},
  year   = {2026}
}

Comments

6 pages, 4 figures