{"paper":{"title":"Brieskorn spheres, cyclic group actions and the Milnor conjecture","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"David Baraglia, Pedram Hekmati","submitted_at":"2022-08-10T04:40:44Z","abstract_excerpt":"In this paper we further develop the theory of equivariant Seiberg-Witten-Floer cohomology of the two authors, with an emphasis on Brieskorn homology spheres. We obtain the following applications. First, we show that the knot concordance invariants $\\theta^{(c)}$ defined by the first author satisfy $\\theta^{(c)}(T_{a,b}) = (a-1)(b-1)/2$ for torus knots, whenever $c$ is a prime not dividing $ab$. Since $\\theta^{(c)}$ is a lower bound for the slice genus, this gives a new proof of the Milnor conjecture of a similar flavour to the proofs using the Ozsv\\'ath-Szab\\'o $\\tau$-invariant or Rasmussen $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05143","kind":"arxiv","version":3},"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/2208.05143/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"}