{"paper":{"title":"Equivariant Cosheaves and Finite Group Representations in Graphic Statics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AT","authors_text":"Bernd Schulze, Miguel Lopez, Zoe Cooperband","submitted_at":"2024-01-17T18:09:23Z","abstract_excerpt":"This work extends the theory of reciprocal diagrams in graphic statics to frameworks that are invariant under finite group actions by utilizing the homology and representation theory of cellular cosheaves, recent tools from applied algebraic topology. By introducing the structure of an equivariant cellular cosheaf, we prove that pairs of self-stresses and reciprocal diagrams of symmetric frameworks are classified by the irreducible representations of the underlying group. We further derive the symmetry-aligned Euler characteristics of a finite dimensional equivariant chain complex, which for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.09392","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/2401.09392/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"}