Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Lyndon's identity theorem for one-relator monoids   For every one-relator monoid $M = \langle A \mid u=v \rangle$ with $u, v \in
A^*$ we construct a contractible $M$-CW complex and use it to build a
projective resolution of the trivial module which is finitely generated in all
dimensions. This proves that all one-relator monoids are of type ${\rm
FP}_\infty$, answering positively a problem posed by Kobayashi in 2000. We also
apply our results to classify the one-relator monoids of cohomological
dimension at most $2$, and to describe the relation module, in the sense of
Ivanov, of a torsion-free one-relator monoid presentation as an explicitly
given principal left ideal of the monoid ring. In addition, we prove the
topological analogues of these results by showing that all one-relator monoids
satisfy the topological finiteness property ${\rm F}_\infty$, and classifying
the one-relator moniods with geometric dimension at most $2$. These results
give a natural monoid analogue of Lyndon's Identity Theorem for one-relator
groups.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol