{"paper":{"title":"Higher homotopy operations and Andr\\'{e}-Quillen cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"David Blanc (U. Haifa), James M. Turner (Calvin College), Mark W. Johnson (Penn State Altoona)","submitted_at":"2011-07-20T20:32:08Z","abstract_excerpt":"There are two main approaches to the problem of realizing a $\\Pi$-algebra (a graded group $\\Lambda$ equipped with an action of the primary homotopy operations) as the homotopy groups of a space $X$. Both involve trying to realize an algebraic free simplicial resolution $G_\\bullet$ of $\\Lambda$ by a simplicial space $W_\\bullet$ and proceed by induction on the simplicial dimension. The first provides a sequence of Andr\\'{e}-Quillen cohomology classes in $H_{AQ}^{n+2}(\\Lambda;\\Omega^{n}\\Lambda)$ for $n \\geq 1$ as obstructions to the existence of successive Postnikov sections for $W_\\bullet$ by wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4117","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"}