{"paper":{"title":"Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniel Hartman, David Gabai, David T. Gay","submitted_at":"2025-05-17T17:08:42Z","abstract_excerpt":"We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \\times S^{2}$ and in connected sums of $S^{2} \\times S^{2}$. that cannot be homotoped to loops of spheres dual to the standard horizontal spheres. In the sequel [GGH], we will use these techniques to expand upon the applicability of the invariant and prove $\\operatorname{Diff}^{+}(S^{4})$ has an exotic element."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12088","kind":"arxiv","version":2},"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/2505.12088/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"}