Publication Date
1-1-2024
Document Type
Article
Publication Title
Groups, Geometry, and Dynamics
Volume
18
Issue
4
DOI
10.4171/GGD/786
First Page
1403
Last Page
1425
Abstract
The full solenoid over a topological space X is the inverse limit of all finite covers. When X is a compact Hausdorff space admitting a locally path-connected universal cover, we relate the pointed homotopy equivalences of the full solenoid to the abstract commensurator of the fundamental group π1(X). The relationship is an isomorphism when X is an aspherical CW complex. If X is additionally a geodesic metric space and π1(X) is residually finite, we show that this topological model is compatible with the realization of the abstract commensurator as a subgroup of the quasi-isometry group of π1(X). This is a general topological analog of work of Biswas, Nag, Odden, Sullivan, and others on the universal hyperbolic solenoid, the full solenoid over a closed surface of genus at least two.
Funding Number
DMS-1547292
Funding Sponsor
Azrieli Foundation
Keywords
abstract commensurator, homotopy equivalence group, quasi-isometry group, solenoid
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Edgar A. Bering and Daniel Studenmund. "Topological models of abstract commensurators" Groups, Geometry, and Dynamics (2024): 1403-1425. https://doi.org/10.4171/GGD/786
