{"paper":{"title":"Fibered Cusp b-Pseudodifferential Operators and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DG","authors_text":"Jun Watanabe","submitted_at":"2019-07-12T05:18:49Z","abstract_excerpt":"Let $X$ be a smooth compact manifold with corners which has two embedded boundary hypersurfaces $\\partial_0 X , \\partial_1 X$, and a fiber bundle $\\phi:\\partial_0 X \\to Y$ is given. By using the method of blowing up, we define a pseudodifferential culculus $\\Psi ^* _{\\Phi,b} (X)$ generalizing the $\\Phi$-calculus of Mazzeo and Melrose and the (small) $b$-calculus of Melrose. We discuss the Fredholm condition of such operators and prove the relative index theorem. And as its application, the index theorem of \"non-closed\" $\\mathbb{Z}/k$ - manifolds is proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05578","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"}