{"paper":{"title":"Existence of $B^k_{\\alpha,\\beta}$-Structures on $C^k$-Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rodney Josu\\'e Biezuner, Yuri Ximenes Martins","submitted_at":"2019-08-13T00:02:39Z","abstract_excerpt":"In this paper we introduce $B_{\\alpha,\\beta}^{k}$-manifolds as generalizations of the notion of smooth manifolds with $G$-structure or with $k$-bounded geometry. These are $C^{k}$-manifolds whose transition functions $\\varphi_{ji}=\\varphi_{j}\\circ\\varphi_{i}^{-1}$ are such that $\\partial^{\\mu}\\varphi_{ji}\\in B_{\\alpha(r)}\\cap C^{k-\\beta(r)}$ for every $\\vert\\mu\\vert=r$, where $B=(B_{r})_{r\\in\\Gamma}$ is some sequence of presheaves of Fr\\'echet spaces endowed with further structures, $\\Gamma\\subset\\mathbb{Z}_{\\geq0}$ is some parameter set and $\\alpha,\\beta$ are functions. We present embedding t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04442","kind":"arxiv","version":3},"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/1908.04442/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"}