{"paper":{"title":"An Oka principle for Stein G-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CV","authors_text":"Gerald W. Schwarz","submitted_at":"2016-08-18T02:13:12Z","abstract_excerpt":"Let $G$ be a reductive complex Lie group acting holomorphically on Stein manifolds $X$ and $Y$. Let $p_X\\colon X\\to Q_X$ and $p_Y\\colon Y\\to Q_Y$ be the quotient mappings. Assume that we have a biholomorphism $Q:= Q_X\\to Q_Y$ and an open cover $\\{U_i\\}$ of $Q$ and $G$-biholomorphisms $\\Phi_i\\colon p_X^{-1}(U_i)\\to p_Y^{-1}(U_i)$ inducing the identity on $U_i$. There is a sheaf of groups $\\mathcal A$ on $Q$ such that the isomorphism classes of all possible $Y$ is the cohomology set $H^1(Q,\\mathcal A)$. The main question we address is to what extent $H^1(Q,\\mathcal A)$ contains only topological "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05156","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"}