{"paper":{"title":"A note on Gorenstein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Steve Halperin, Yves Felix","submitted_at":"2018-12-23T10:39:13Z","abstract_excerpt":"Associated with an augmented differential graded algebra $R= R^{\\geq 0}$ is a homotopy invariant ${\\mathcal T}(R)$. This is a graded vector space, and if $H^0(R)$ is the ground field and $H^{>N}(R)= 0$ then dim$\\, {\\mathcal T}(R)= 1$ if and only if $H(R)$ is a Poincar\\'e duality algebra. In the case of Sullivan extensions $\\land W\\to \\land W\\otimes \\land Z\\to \\land Z$ in which dim$\\, H(\\land Z)<\\infty$ we show that $${\\mathcal T}(\\land W\\otimes \\land Z)= {\\mathcal T}(\\land W)\\otimes {\\mathcal T}(\\land Z).$$ This is applied to finite dimensional CW complexes $X$ where the fundamental group $G$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09686","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":""},"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"}