{"paper":{"title":"Swap action on moduli spaces of polygonal linkages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Gaiane Panina, Mikhail Khristoforov","submitted_at":"2011-07-01T07:32:42Z","abstract_excerpt":"The basic object of the paper is the moduli space $M_{2,3}(L)$ of a closed polygonal linkage either in $\\mathbb{R}^2$ or in $\\mathbb{R}^3$. As was originally suggested by G. Khimshiashvili, the space $M_{2}(L)$ is equipped with the oriented area function $A$, whereas (as is suggested in the paper) $M_{3}(L)$ is equipped with the vector area function $S$. The latter are generically Morse functions, whose critical points have a nice description. In the preprint, we define a \\textit{swap action} (that is, the action of some group generated by edge transpositions) on the space $M_{2,3}(L)$ which p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0126","kind":"arxiv","version":2},"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"}