Geometry and Topology, Group theory
Free inverse monoids are not ${\mathrm{FP}}_{2}$
Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 1047-1057.

We give a topological proof that a free inverse monoid on one or more generators is neither of type left-${\mathrm{FP}}_{2}$ nor right-${\mathrm{FP}}_{2}$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.

Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.247
Classification: 20M50,  20M18,  20M05,  20J05
Robert D. Gray 1; Benjamin Steinberg 2

1 School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
2 Department of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, New York 10031, USA
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Robert D. Gray; Benjamin Steinberg. Free inverse monoids are not ${\protect \rm FP}_2$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 1047-1057. doi : 10.5802/crmath.247. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.247/

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