Matsumoto, Shigenori A counterexample of \(C^ \infty\) classes to the Seifert conjecture according to K. M. Kuperberg. (Japanese) Zbl 0866.57021 Sugaku 47, No. 1, 38-45 (1995). This exposition reviews the real analytic counterexample to the Seifert conjecture due to K. M. Kuperberg [Ann. Math., II. Ser. 140, 723-732 (1994; Zbl 0856.57024)], on the existence of periodic orbits in flows on the three-dimensional sphere \(S^3\). Kuperberg’s simple and beautiful idea is clearly explained with a short history of the study and with numerical experiments by E. Ghys, B. Sevennec. See also [G. Kuperberg, K. Kuperberg, ibid. 143, 547-576; corr. reprint 144, 239-268 (1996; Zbl 0856.57026)]. Reviewer: G.Ishikawa (Sapporo) Cited in 1 Review MSC: 57R22 Topology of vector bundles and fiber bundles Keywords:Seifert conjecture; periodic orbits Citations:Zbl 0856.57024; Zbl 0856.57026 × Cite Format Result Cite Review PDF