{"paper":{"title":"Range decreasing group homomorphisms and holomorphic maps between generalized loop spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.FA","math.RT"],"primary_cat":"math.CV","authors_text":"Ning Zhang","submitted_at":"2021-02-11T17:59:29Z","abstract_excerpt":"Let $\\mathcal{G}$ resp. $M$ be a positive dimensional Lie group resp. connected complex manifold without boundary and $V$ a finite dimensional $C^{\\infty}$ compact connected manifold, possibly with boundary. Fix a smoothness class $\\mathcal{F}=C^{\\infty}$, H\\\"older $C^{k, \\alpha}$ or Sobolev $W^{k, p}$. The space $\\mathcal{F}(V, \\mathcal{G})$ resp. $\\mathcal{F}(V, M)$ of all $\\mathcal{F}$ maps $V \\to \\mathcal{G}$ resp. $V \\to M$ is a Banach/Fr\\'echet Lie group resp. complex manifold. Let $\\mathcal{F}^0(V, \\mathcal{G})$ resp. $\\mathcal{F}^{0}(V, M)$ be the component of $\\mathcal{F}(V, \\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06157","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.06157/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}