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Article Dans Une Revue L'Enseignement Mathématique Année : 2020

On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$

Résumé

In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\mathrm{Homeo}(D,\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\mathrm{Homeo}(D,\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.

Dates et versions

hal-02955611 , version 1 (02-10-2020)

Identifiants

Citer

Michele Triestino. On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$. L'Enseignement Mathématique , 2020, 66 (3), pp.409-418. ⟨10.4171/LEM/66-3/4-5⟩. ⟨hal-02955611⟩
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