1. Topological models of abstract commensurators.
- Author
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Bering IV, Edgar A. and Studenmund, Daniel
- Subjects
METRIC spaces ,TOPOLOGICAL spaces ,HAUSDORFF spaces ,GEODESIC spaces ,HOMOTOPY groups - 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 π
1 (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. [ABSTRACT FROM AUTHOR]- Published
- 2024
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