Work

Reversibility and its asymptotic counting in Picard group

Year: 2026

Type: preprint

Abstract: We investigate reversible elements in the Picard modular group $\mathrm{PSL}(2,\mathbb{Z}[i])$. We show that reversibility coincides with strong reversibility for Kleinian groups, in particular for the Picard group. We classify reversible elements in the Picard group and characterize loxodromic reversible elements up to conjugacy. We prove that each such conjugacy class contains exactly eight special representatives. We also obtain asymptotic estimates for the number of reversible conjugacy classes with bounded trace.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11398

Authors: Das, Debattam, Gongopadhyay, Krishnendu, Mukhopadhyay, Anirban

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212239900

Cites: 6

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Related to: 10