Free inverse monoids are not ${\protect \rm FP}_2$

Robert D. Gray; Benjamin Steinberg

doi:10.5802/crmath.247

Geometry and Topology, Group theory

Free inverse monoids are not

{FP}_{2}

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

Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 1047-1057.

Abstract

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

Received: 2020-07-03
Revised: 2020-12-16
Accepted: 2021-07-23
Published online: 2021-10-08

DOI: 10.5802/crmath.247

Classification: 20M50, 20M18, 20M05, 20J05

Author's affiliations:

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Free inverse monoids are not ${\protect \rm FP}_2$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1047--1057},
     publisher = {Acad\'emie des sciences, Paris},
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     number = {8},
     year = {2021},
     doi = {10.5802/crmath.247},
     language = {en},
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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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