Work

Systoles of Arithmetic Hyperbolic 2- and 3-Manifolds

Year: 2025

Type: article

Abstract: In this paper we study the systoles of arithmetic hyperbolic 2 - and 3 -manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2 - and 3 -manifolds which are pairwise noncommensurable, all have the same systole, and whose volumes are explicitly bounded. Our second result fixes a positive number x and gives an upper bound for the least volume of an arithmetic hyperbolic 2 - or 3 -manifold whose systole is greater than x . We conclude by determining, for certain small values of x , the least volume of a principal arithmetic hyperbolic 2 -manifold over ℚ or 3 -manifold over ℚ ( i ) whose systole is greater than x .

Source: Annales de la faculté des sciences de Toulouse Mathématiques

DOI: 10.5802/afst.1793

Authors: Rainie Bozzai, Benjamin Linowitz

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: G653274256, RUI: The Geometry of Arithmetic Locally Symmetric Spaces, Graduate Research Fellowship Program (GRFP)

OpenAlex ID: W4407103114

FWCI:

Cites: 29

Cited by:

Related to: 10