{"paper":{"title":"Equivariant trisections for group actions on four-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Evan Scott, Jeffrey Meier","submitted_at":"2025-01-29T21:18:19Z","abstract_excerpt":"Let $G$ be a finite group, and let $X$ be a smooth, orientable, connected, closed 4-dimensional $G$-manifold.\n  Let $\\mathcal{S}$ be a smooth, embedded, $G$-invariant surface in $X$.\n  We introduce the concept of a $G$-equivariant trisection of $X$ and the notion of $G$-equivariant bridge trisected position for $\\mathcal{S}$ and establish that any such $X$ admits a $G$-equivariant trisection such that $\\mathcal{S}$ is in equivariant bridge trisected position.\n  Our definitions are designed so that $G$-equivariant (bridge) trisections are determined by their spines; hence, the 4-dimensional equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.17999","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.17999/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"}