{"paper":{"title":"Unbounded Gaps Between Ordinary and Equivariant Dehn Surgery Numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Chunxing Yan, Qilong Guo","submitted_at":"2026-08-04T16:22:11Z","abstract_excerpt":"For a closed oriented $3$-manifold $Y$ and an orientation-preserving involution $\\tau$, let $\\DS(Y)$ denote the minimum number of components in an integral surgery description of $Y$, and let $\\EDS(Y,\\tau)$ denote the corresponding minimum among periodic surgery descriptions inducing $\\tau$. We prove that for every integer $k\\geq 1$ there is a pair $(Y_k,\\tau_k)$ such that \\[\n  \\DS(Y_k)=k,\n  \\qquad\n  \\EDS(Y_k,\\tau_k)=2k. \\] Consequently, the difference $\\EDS(Y,\\tau)-\\DS(Y)$ is unbounded even when $\\tau$ is an involution. This answers Problems~1.15(b) and~1.15(c) in the K3 problem list. We also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03886","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/2608.03886/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"}