The full spectrum of scl on recursively presented groups

2019/09/03 by Nicolaus Heuer, Heuer, Nicolaus · 2 citations
Computer Science · Mathematics · #20F06 #20F10 #20F65 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F06 #msc:20F10 #msc:20F65

paper · pdf · doi:10.48550/arxiv.1909.01309

comments welcome

arxiv created 2019/09/03 · openalex publication_date 2019/09/03 · arxiv updated 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the set SCL^rp of stable commutator lengths on recursively presented groups equals the set of non-negative right-computable numbers. Hence all non-negative algebraic or computable numbers are in SCL^rp and SCL^rp is not closed under subtraction. We also show that every non-negative real number is the stable commutator length of an element in some infinitely presented small cancellation group.

Citations

• Surface subgroups of right-angled Artin groups

Cited by

• Algebraic irrational stable commutator length in finitely presented groups
• Computing commutator length is hard

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