PreprintCC BY 4.0arXiv
Mapping class groups of solenoidal manifolds
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.
Related
- On the mapping class groups of simply connected smooth 4-manifolds
- Mapping class groups of negatively curved four-manifolds
- A survey on mapping class groups of 3-manifolds
- Topological mapping class groups of non-simply connected 4-manifolds
- Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology
BibTeX
@misc{hurder2026mapping,
title = {{Mapping class groups of solenoidal manifolds}},
author = {Steven Hurder and Olga Lukina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20131},
eprint = {2610.20131},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20131},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mapping class groups of solenoidal manifolds
AU - Steven Hurder
AU - Olga Lukina
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20131
UR - https://arxiv.org/abs/2610.20131
AB - 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.
ER -