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- W2969832046 abstract "A left-order on a group $G$ is a total order $<$ on $G$ such that for any $f$, $g$ and $h$ in $G$ we have $f < g Leftrightarrow hf < hg$. We construct a finitely generated subgroup $G$ of $operatorname{Homeo} (I^2;delta I^2)$, the group of those homeomorphisms of the disc that fix the boundary pointwise, and show $G$ does not admit a left-order. Since any left-order on $operatorname{Homeo} (I^2;delta I^2)$ would restrict to a left-order on $G$ this shows that $operatorname{Homeo} (I^2;delta I^2)$ does not admit a left-order. Since $operatorname{Homeo} (I;delta I)$ admits a left-order it follows that neither $G$ nor $operatorname{Homeo} (I^2;delta I^2)$ embed in $operatorname{Homeo} (I;delta I)$." @default.
- W2969832046 created "2019-08-29" @default.
- W2969832046 creator A5089595324 @default.
- W2969832046 date "2019-01-01" @default.
- W2969832046 modified "2023-10-16" @default.
- W2969832046 title "The group of boundary fixing homeomorphisms of the disc is not left-orderable" @default.
- W2969832046 doi "https://doi.org/10.4007/annals.2019.190.2.5" @default.
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