{"paper":{"title":"Fine projection complex and subsurface homeomorphisms with positive stable commutator length","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface.","cross_cats":["math.DS","math.GR"],"primary_cat":"math.GT","authors_text":"Yongsheng Jia, Yusen Long","submitted_at":"2026-04-14T17:08:10Z","abstract_excerpt":"Drawing inspiration from [BBF15], we construct a family of unbounded quasi-trees for a connected closed oriented surface $S_g$ of genus $g\\geq 2$, upon which the group $\\mathrm{Homeo}_0(S_g)$ acts coboundedly by isometries. As an application, we show that some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in $\\mathrm{Homeo}_0(S_g)$. Moreover, we provide a version of projection complex that does not require the finiteness condition."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in Homeo_0(S_g)","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The family of unbounded quasi-trees exists with the stated cobounded isometric action for every closed oriented surface of genus g >= 2, and the projection complex construction succeeds without the usual finiteness conditions on the subsurface data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A finiteness-free projection complex yields unbounded quasi-trees for Homeo_0(S_g) with cobounded isometric actions, proving positive scl for subsurface-preserving homeomorphisms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8e5d41e8c794c17009929756acdd0c39835718ca131e462487fc88fd81b10f15"},"source":{"id":"2604.12974","kind":"arxiv","version":2},"verdict":{"id":"0f4f21f8-2293-433d-bb27-00512d600fcb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T13:51:21.566805Z","strongest_claim":"some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in Homeo_0(S_g)","one_line_summary":"A finiteness-free projection complex yields unbounded quasi-trees for Homeo_0(S_g) with cobounded isometric actions, proving positive scl for subsurface-preserving homeomorphisms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The family of unbounded quasi-trees exists with the stated cobounded isometric action for every closed oriented surface of genus g >= 2, and the projection complex construction succeeds without the usual finiteness conditions on the subsurface data.","pith_extraction_headline":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.12974/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}