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• W2898681169 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.
• W2898681169 created "2018-11-09" @default.
• W2898681169 creator A5089595324 @default.
• W2898681169 date "2018-10-30" @default.
• W2898681169 modified "2023-09-27" @default.
• W2898681169 title "The Group of Boundary Fixing Homeomorphisms of the Disc is Not Left-Orderable" @default.
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