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arXiv · 2110.06286

Algebraic irrational stable commutator length in finitely presented groups

Francesco Fournier-Facio·Yash Lodha
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Abstract

We provide the first example of a finitely presented (in fact, type $F_\infty$) group with elements whose stable commutator length is algebraic and irrational, answering a question of Calegari. Our example is the lift to the real line of the \emph{golden ratio Thompson group} $T_\tau$: the circle analogue of the Cleary's golden ratio Thompson group $F_\tau$ which acts on the interval.

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Francesco Fournier-Facio, Yash Lodha. 2021-10-12. Algebraic irrational stable commutator length in finitely presented groups. https://arxiv.org/abs/2110.06286

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