Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lamplighters admit weakly aperiodic SFTs   Let $A$ be a finite set and $G$ a group. A closed subset $X$ of $A^G$ is
called a subshift if the action of $G$ on $A^G$ preserves $X$. If $K$ is a
closed subset of $A^G$ such that membership in $K$ is determined by looking at
a fixed finite set of coordinates, and $X$ is the intersection of all
translates of $K$ under the action of $G$, then $X$ is called a subshift of
finite type (SFT). If an SFT is nonempty and contains no finite $G$-orbits, it
is said to be weakly aperiodic. A virtually cyclic group has no weakly
aperiodic SFT, and Carroll and Penland have conjectured that a group with no
weakly aperiodic SFT must be virtually cyclic. Answering a question of Jeandel,
we show that lamplighters always admit weakly aperiodic SFTs.

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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con