Algebraic irrational stable commutator length in finitely presented groups

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.

12 pages. This paper is subsumed by the following preprint of the authors: arXiv:2111.07931. Any reader interested only in the results for stable commutator length may find it easier to start here

References in corpus (4)

• Uniform symplicity of groups with proximal action
• Scl in graphs of groups
• The full spectrum of scl on recursively presented groups
• Irrational-slope versions of Thompson's groups $T$ and $V$