{"paper":{"title":"String Topology, Euler Class and TNCZ free loop fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Luc Menichi (LAREMA)","submitted_at":"2013-08-30T09:02:59Z","abstract_excerpt":"Let $M$ be a connected, closed oriented manifold. Let $\\omega\\in H^m(M)$ be its orientation class. Let $\\chi(M)$ be its Euler characteristic. Consider the free loop fibration $\\Omega M\\buildrel{i}\\over\\hookrightarrow LM\\buildrel{ev}\\over\\twoheadrightarrow M$. For any class $a\\in H^*(LM)$ of positive degree, we prove that the cup product $\\chi(M)a\\cup ev^*(\\omega)$ is null. In particular, if $i^*:H^*(LM;\\mathbb{F}_p)\\twoheadrightarrow H^*(\\Omega M;\\mathbb{F}_p)$ is onto then $\\chi(M)$ is divisible by $p$ (or $M$ is a point)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6684","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"}