Work

Geometric and arithmetic properties of Löbell polyhedra

Year: 2025

Type: article

Abstract: The Löbell polyhedra form an infinite family of compact right-angled hyperbolic polyhedra in dimension 3. We observe, through both elementary and more conceptual means, that the "systoles" of the Löbell polyhedra approach 0, so that these polyhedra give rise to particularly straightforward examples of closed hyperbolic 3-manifolds with arbitrarily small systole, and constitute an infinite family even up to commensurability.By computing number-theoretic invariants of these polyhedra, we refine the latter result, and also determine precisely which of the Löbell polyhedra are quasi-arithmetic.

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2025.25.2281

Authors: Nikolay Bogachev, Sami Douba

Institutions: University of Toronto, Institute for Information Transmission Problems, University of Toronto Scarborough, Institut des Hautes Études Scientifiques

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Russian Science Foundation, Institut des Hautes Études Scientifiques, Université Paris-Saclay

Award: G5431845024