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- W4297802912 abstract "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." @default.
- W4297802912 created "2022-10-01" @default.
- W4297802912 creator A5056602969 @default.
- W4297802912 creator A5071805357 @default.
- W4297802912 date "2019-10-22" @default.
- W4297802912 modified "2023-09-26" @default.
- W4297802912 title "A Lyndon's identity theorem for one-relator monoids" @default.
- W4297802912 doi "https://doi.org/10.48550/arxiv.1910.09914" @default.
- W4297802912 hasPublicationYear "2019" @default.
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