{"paper":{"title":"Homotopy principles for equivariant isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CV","authors_text":"Finnur Larusson, Frank Kutzschebauch, Gerald W. Schwarz","submitted_at":"2015-03-03T01:19:39Z","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. When is there an equivariant biholomorphism of $X$ and $Y$? A necessary condition is that the categorical quotients $Q_X$ and $Q_Y$ are biholomorphic and that the biholomorphism $\\phi$ sends the Luna strata of $Q_X$ isomorphically onto the corresponding Luna strata of $Q_Y$. Fix $\\phi$. We demonstrate two homotopy principles in this situation. The first result says that if there is a $G$-diffeomorphism $\\Phi\\colon X\\to Y$, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00797","kind":"arxiv","version":4},"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"}