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arXiv · 1909.01877

On diagram groups over Fibonacci-like semigroup presentations and their generalizations

Victor Guba
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Abstract

We answer the question by Matt Brin on the structure of diagram groups over semigroup presentation ${\mathcal P}=\langle a,b,c\mid a=bc,b=ca,c=ab\rangle$. In the talk on Oberwolfach workshop, Brin conjectured that the diagram group over $\mathcal P$ with base $a$ is isomorphic to the generalized Thompson's group $F_9$. We confirm this conjecture and consider some generalizations of this fact.

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Victor Guba. 2019-09-03. On diagram groups over Fibonacci-like semigroup presentations and their generalizations. https://arxiv.org/abs/1909.01877

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