6533b829fe1ef96bd128a4fb

RESEARCH PRODUCT

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

Michele Triestino

subject

CombinatoricsGroup (mathematics)Primary 37C85. Secondary 37E05 37E10 37E20[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]FOS: MathematicsBoundary (topology)Finitely-generated abelian groupGroup Theory (math.GR)Dynamical Systems (math.DS)Mathematics - Dynamical SystemsMathematics - Group Theory[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Mathematics

description

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.

yearjournalcountryeditionlanguage
2020-01-01
http://arxiv.org/abs/1912.05386