Free inverse monoids are not $FP_2$
Robert D. Gray, Benjamin Steinberg
TL;DR
This paper proves that free inverse monoids with one or more generators lack certain finiteness properties, specifically not being of type left-$FP_2$ or right-$FP_2$, extending classical non-finite presentation results.
Contribution
It provides a topological proof that free inverse monoids are not of type left-$FP_2$ or right-$FP_2$, strengthening previous results on their non-finite presentability.
Findings
Free inverse monoids are not of type left-$FP_2$ or right-$FP_2$
The proof uses topological methods
Extends classical non-finite presentation results
Abstract
We give a topological proof that a free inverse monoid on one or more generators is neither of type left- nor right-. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Geometric and Algebraic Topology · Advanced Topology and Set Theory