Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Group of Boundary Fixing Homeomorphisms of the Disc is Not
  Left-Orderable   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
$\operatorname{Homeo} (I;\delta I)$.

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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph