Projects per year
Abstract
For every onerelator monoid M=⟨A∣u=v⟩ with u,v∈A∗ we construct a contractible MCW complex and use it to build a projective resolution of the trivial module which is finitely generated in all dimensions. This proves that all onerelator monoids are of type FP∞, answering positively a problem posed by Kobayashi in 2000. We also apply our results to classify the onerelator monoids of cohomological dimension at most 2, and to describe the relation module, in the sense of Ivanov, of a torsionfree onerelator 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 onerelator monoids satisfy the topological finiteness property F∞, and classifying the onerelator monoids with geometric dimension at most 2. These results give a natural monoid analogue of Lyndon’s Identity Theorem for onerelator groups.
Original language  English 

Article number  59 
Journal  Selecta Mathematica 
Volume  28 
Issue number  3 
DOIs  
Publication status  Published  27 Apr 2022 
Keywords
 Classifying space
 Cohomological dimension
 Geometric dimension
 Homological finiteness property
 Onerelator monoid
Projects
 2 Finished

Topological and homological properties of onerelator monoids
London Mathematical Society (The)
1/04/19 → 30/09/19
Project: Research