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.
1
San José State University, San José, USA
2
Binghamton University, Binghamton, USA
Edgar A. Bering IV; Daniel Studenmund. Topological models of abstract commensurators. Groups, geometry, and dynamics, Tome 18 (2024) no. 4, pp. 1403-1425. doi: 10.4171/ggd/786
@article{10_4171_ggd_786,
author = {Edgar A. Bering IV and Daniel Studenmund},
title = {Topological models of abstract commensurators},
journal = {Groups, geometry, and dynamics},
pages = {1403--1425},
year = {2024},
volume = {18},
number = {4},
doi = {10.4171/ggd/786},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/786/}
}
TY - JOUR
AU - Edgar A. Bering IV
AU - Daniel Studenmund
TI - Topological models of abstract commensurators
JO - Groups, geometry, and dynamics
PY - 2024
SP - 1403
EP - 1425
VL - 18
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/786/
DO - 10.4171/ggd/786
ID - 10_4171_ggd_786
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/786/
%R 10.4171/ggd/786
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