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A smooth counterexample to the Seifert conjecture. (English) Zbl 0856.57024

Ann. Math. (2) 140, No. 3, 723-732 (1994).

Developing an ingenious construction of a \(C^\infty\) aperiodic plug in dimension three, the author offers a counterexample to the Seifert conjecture: every nonsingular continuous vector field on \(S^3\) has a closed integral curve. In fact the answer of the author is the following (Theorem 5.1): There exists on \(S^3\) a \(C^\infty\) dynamical system with no compact orbits.

Reviewer: I.D.Albu (Timişoara)

Cited in 3 Reviews

Cited in 34 Documents

MSC:

57R25

Vector fields, frame fields in differential topology

Keywords:

flow; mirror-image plus; Wilson-type plug; self-insertions; aperiodic plug; Seifert conjecture; dynamical system; compact orbits

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