{"paper":{"title":"Abelian gerbes, generalized geometries and foliations of small exotic R^4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.GT","math.MP"],"primary_cat":"hep-th","authors_text":"Jerzy Kr\\'ol, Torsten Asselmeyer-Maluga","submitted_at":"2009-04-08T07:41:57Z","abstract_excerpt":"In the paper we prove the existence of the strict but relative relation between small exotic $\\mathbb{R}^{4}$ for a fixed radial family of DeMichelis-Freedman type, and cobordism classes of codimension one foliations of $S^{3}$ distinguished by the Godbillon-Vey invariant, $GV\\in H^{3}(S^{3},\\mathbb{R})$ (represented by a 3-form). This invariant can be integrated to get the Godbillon-Vey number. For a fixed radial family, we will show that the isotopy classes (invariance w.r.t. small diffeomorphisms or coordinate transformations) of all members in this family are distinguished by the Godbillon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1276","kind":"arxiv","version":5},"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"}