{"paper":{"title":"The $g$-areas and the commutator length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Andrei Teleman, Fran\\c{c}ois Lalonde","submitted_at":"2014-04-03T16:55:18Z","abstract_excerpt":"The commutator length of a Hamiltonian diffeomorphism $f\\in \\mathrm{Ham}(M, \\omega)$ of a closed symplectic manifold $(M,\\omega)$ is by definition the minimal $k$ such that $f$ can be written as a product of $k$ commutators in $\\mathrm{Ham}(M, \\omega)$. We introduce a new invariant for Hamiltonian diffeomorphisms, called the $k_+$-area, which measures the \"distance\", in a certain sense, to the subspace $\\mathcal{C}_k$ of all products of $k$ commutators. Therefore this invariant can be seen as the obstruction to writing a given Hamiltonian diffeomorphism as a product of $k$ commutators. We also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1004","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"}