Commability and focal locally compact groups
Yves Cornulier

TL;DR
This paper introduces the concept of commability for locally compact groups, classifies focal hyperbolic groups under this relation, and identifies a real parameter as a quasi-isometry invariant in the mixed case.
Contribution
It defines commability for locally compact groups and provides a classification of focal hyperbolic groups up to this relation, highlighting a key invariant.
Findings
Classification of focal hyperbolic locally compact groups up to commability
Identification of a real parameter as a quasi-isometry invariant in the mixed case
Establishment of commability as an equivalence relation involving cocompact inclusions and quotients
Abstract
We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact groups up to commability. In the mixed case, it involves a real parameter, which is shown to be a quasi-isometry invariant.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows
