Algebraic irrational stable commutator length in finitely presented groups

2021/10/12 by Francesco Fournier-Facio, Fournier-Facio, Francesco, Yash Lodha +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR

paper · pdf · doi:10.48550/arxiv.2110.06286

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

openalex publication_date 2021/10/12 · arxiv created 2021/11/16 · arxiv updated 2021/11/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We provide the first example of a finitely presented (in fact, type F_∞) 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 golden ratio Thompson group T_τ: the circle analogue of the Cleary's golden ratio Thompson group F_τ which acts on the interval.

Citations

• The full spectrum of scl on recursively presented groups
• Second bounded cohomology of groups acting on 1-manifolds and\n applications to spectrum problems

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