Work

Mapping class groups of solenoidal manifolds

Year: 2026

Type: preprint

Abstract: The goal of this work is to calculate the mapping class groups of solenoidal manifolds. We introduce the dynamical commensurator group associated to an odometer action, and develop methods to calculate the mapping class group using the dynamical commensurator. Our results generalize the previous results of Odden for the mapping class group of the universal solenoid over a Riemann surface, and of Bering and Studenmund for the pointed mapping class group of the universal solenoid over a compact aspherical manifold. We include a selection of examples.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.20131

Authors: Hurder, Steven, Lukina, Olga

Institutions: University of Illinois Chicago, Leiden University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Award: Three facets of laminated dynamical systems (3-FOLDS)

OpenAlex ID: W7222314538

Cites: 3

Cited by:

Related to: 10