{"paper":{"title":"Algebraic Hopf invariants and rational models for mapping spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Felix Wierstra","submitted_at":"2016-12-22T19:28:44Z","abstract_excerpt":"In this paper we will define an invariant $mc_{\\infty}(f)$ of maps $f:X \\rightarrow Y_{\\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\\mathbb{Q}}$. We prove that this invariant is complete, i.e. $mc_{\\infty}(f)=mc_{\\infty}(g)$ if an only if $f$ and $g$ are homotopic. We will also construct an $L_{\\infty}$-model for the based mapping space $Map_*(X,Y_{\\mathbb{Q}})$ from a $C_{\\infty}$-coalgebra and an $L_{\\infty}$-algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07762","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"}