{"paper":{"title":"Filtered Hirsch Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Samson Saneblidze","submitted_at":"2007-07-16T07:36:11Z","abstract_excerpt":"Motivated by the cohomology theory of loop spaces, we consider a special class of higher order homotopy commutative differential graded algebras and construct the filtered Hirsch model for such an algebra $A$. When $x\\in H(A)$ with $\\mathbb{Z}$ coefficients and $x^{2}=0,$ the symmetric Massey products $% \\langle x\\rangle ^{n}$ with $n\\geq 3$ have a finite order (whenever defined). However, if $\\Bbbk $ is a field of characteristic zero, $\\langle x\\rangle ^{n}$ is defined and vanishes in $H(A\\otimes \\Bbbk )$ for all $n$. If $p$ is an odd prime, the Kraines formula $\\langle x\\rangle ^{p}=-\\beta \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2165","kind":"arxiv","version":12},"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"}