{"paper":{"title":"Polyfold and Fredholm Theory I: Basic Theory in M-Polyfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.FA","authors_text":"Eduard Zehnder, Helmut H. Hofer, Kris Wysocki","submitted_at":"2014-07-11T14:58:04Z","abstract_excerpt":"The main topic is the development of a Fredholm theory in a new class of spaces called M-polyfolds. In the subsequent Volume II the theory will be generalized to an even larger class of spaces called polyfolds, which can also incorporate local symmetries. The whole package provides a functional analytic framework to deal with compactness and transversality issues as they occur in moduli problems of symplectic geometry. Applications of the theory cover Floer-type theories as they occur in symplectic geometry. M-polyfolds and the more general polyfolds are smooth spaces which can be finite-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3185","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"}