{"paper":{"title":"Gaps in scl for Amalgamated Free Products and RAAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Nicolaus Heuer","submitted_at":"2018-02-04T10:45:35Z","abstract_excerpt":"We develop a new criterion to tell if a group $G$ has the maximal gap of $1/2$ in stable commutator length (scl). For amalgamated free products $G = A \\star_C B$ we show that every element $g$ in the commutator subgroup of $G$ which does not conjugate into $A$ or $B$ satisfies $scl(g) \\geq 1/2$, provided that $C$ embeds as a left relatively convex subgroup in both $A$ and $B$. We deduce from this that every non-trivial element $g$ in the commutator subgroup of a right-angled Artin group $G$ satisfies $scl(g) \\geq 1/2$. This bound is sharp and is inherited by all fundamental groups of special c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01107","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}