{"paper":{"title":"Representing de Rham cohomology classes on an open Riemann surface by holomorphic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antonio Alarcon, Finnur Larusson","submitted_at":"2017-04-10T23:13:19Z","abstract_excerpt":"Let $X$ be a connected open Riemann surface. Let $Y$ be an Oka domain in the smooth locus of an analytic subvariety of $\\mathbb C^n$, $n\\geq 1$, such that the convex hull of $Y$ is all of $\\mathbb C^n$. Let $\\mathscr O_*(X, Y)$ be the space of nondegenerate holomorphic maps $X\\to Y$. Take a holomorphic $1$-form $\\theta$ on $X$, not identically zero, and let $\\pi:\\mathscr O_*(X,Y) \\to H^1(X,\\mathbb C^n)$ send a map $g$ to the cohomology class of $g\\theta$. Our main theorem states that $\\pi$ is a Serre fibration. This result subsumes the 1971 theorem of Kusunoki and Sainouchi that both the perio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03082","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"}