Stable commutator length in right-angled Artin groups
Problem. Let G be a right-angled Artin group. Is the stable commutator length scl(g) a rational number for every g ∈ [G, G]? For free groups this is true by Calegari’s Rationality Theorem. (See 18.40 for the definition of scl(g).). This is Kourovka Notebook Problem \(21.127\).
1Status
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In TheoremDB, research kourovka-21-127-stable-commutator-length-in-right-angled-artin-groups: "Stable commutator length in right-angled Artin groups". Call orient with problem_ref "kourovka-21-127-stable-commutator-length-in-right-angled-artin-groups", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- Outer order automorphisms of Dlab groupskourovka notebook
- Distributive lattices of right-relatively convex subgroupskourovka notebook
- Embedding groups of type F into higher finiteness typeskourovka notebook
How to cite
TheoremDB contributors, “Stable commutator length in right-angled Artin groups,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-127-stable-commutator-length-in-right-angled-artin-groupsThis page as plain text: kourovka-21-127-stable-commutator-length-in-right-angled-artin-groups.md
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