{"paper":{"title":"Compactification of the space of branched coverings of the two-dimensional sphere","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"S. Yu. Orevkov, V. I. Zvonilov","submitted_at":"2022-01-09T20:34:48Z","abstract_excerpt":"For a closed oriented surface $ \\Sigma $ we define its degenerations into singular surfaces that are locally homeomorphic to wedges of disks. Let $X_{\\Sigma,n}$ be the set of isomorphism classes of orientation preserving $n$-fold branched coverings $ \\Sigma\\rightarrow S^2 $ of the two-dimensional sphere. We complete $X_{\\Sigma,n}$ with the isomorphism classes of mappings that cover the sphere by the degenerations of $ \\Sigma $. In case $ \\Sigma=S^2$, the topology that we define on the obtained completion $\\bar{X}_{\\Sigma,n}$ coincides on $X_{S^2,n}$ with the topology induced by the space of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.03084","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/2201.03084/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"}