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A counterexample of \(C^ \infty\) classes to the Seifert conjecture according to K. M. Kuperberg. (Japanese) Zbl 0866.57021

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)].

MSC:

57R22 Topology of vector bundles and fiber bundles