{"paper":{"title":"A note on the Nielsen realization problem for K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"David Baraglia, Hokuto Konno","submitted_at":"2019-08-11T23:04:45Z","abstract_excerpt":"We will show the following three theorems on the diffeomorphism and homeomorphism groups of a $K3$ surface. The first theorem is that the natural map $\\pi_{0}(Diff(K3)) \\to Aut(H^{2}(K3;\\mathbb{Z}))$ has a section over its image. The second is that, there exists a subgroup $G$ of $\\pi_{0}(Diff(K3))$ of order two over which there is no splitting of the map $Diff(K3) \\to \\pi_{0}(Diff(K3))$, but there is a splitting of $Homeo(K3) \\to \\pi_{0}(Homeo(K3))$ over the image of $G$ in $\\pi_{0}(Homeo(K3))$, which is non-trivial. The third is that the map $\\pi_{1}(Diff(K3)) \\to \\pi_{1}(Homeo(K3))$ is not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03970","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03970/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"}