{"paper":{"title":"The kernel bundle of a holomorphic Fredholm family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Gerardo A. Mendoza, Thomas Krainer","submitted_at":"2013-01-24T15:17:39Z","abstract_excerpt":"Let $\\Y$ be a smooth connected manifold, $\\Sigma\\subset\\C$ an open set and $(\\sigma,y)\\to\\scrP_y(\\sigma)$ a family of unbounded Fredholm operators $D\\subset H_1\\to H_2$ of index 0 depending smoothly on $(y,\\sigma)\\in \\Y\\times \\Sigma$ and holomorphically on $\\sigma$. We show how to associate to $\\scrP$, under mild hypotheses, a smooth vector bundle $\\kerb\\to\\Y$ whose fiber over a given $y\\in \\Y$ consists of classes, modulo holomorphic elements, of meromorphic elements $\\phi$ with $\\scrP_y\\phi$ holomorphic. As applications we give two examples relevant in the general theory of boundary value pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5811","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"}