Countable modular groups of infinite-type surfaces

In this paper, we prove that every connected, orientable infinite-type surface [Formula: see text] without boundary and finite genus has a Riemann surface structure such that its modular group of quasiconformal homeomorphisms is countable.

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Publication Details

Journal
Journal of Topology and Analysis
Published
2026-05-21
DOI
https://doi.org/10.1142/s1793525326500354
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Countable modular groups of infinite-type surfaces

Rogelio Niño-Hernández
Journal of Topology and Analysis
Geometric and Algebraic Topology
article

Countable modular groups of infinite-type surfaces

Rogelio Niño-Hernández
article en

Abstract

In this paper, we prove that every connected, orientable infinite-type surface [Formula: see text] without boundary and finite genus has a Riemann surface structure such that its modular group of quasiconformal homeomorphisms is countable.

Journal of Topology and Analysis
Universidad Nacional Autónoma de México (MX)
Openalex Percentile: Top 2%
Geometric and Algebraic Topology
DOISourceOpenAlex
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Countable modular groups of infinite-type surfaces — Rogelio Niño-Hernández · Journal of Topology and Analysis (2026) | TGRS Research Map | TGRS