Construction of vector fields without periodic orbits (after Krystyna Kuperberg). (Construction de champs de vecteurs sans orbite périodique (d’après Krystyna Kuperberg).) (French) Zbl 0846.57019

Ghys, Étienne

Séminaire Bourbaki. Volume 1993/94. Exposés 775-789. Paris: Société Mathématique de France, Astérisque. 227, 283-307 (Exp. No. 785) (1995).

This is a very welcome expository paper concerned with the famous Seifert Conjecture. It discusses mainly the following theorem, due to K. Kuperberg: “On any 3-dimensional closed manifold there exists a nonsingular and analytic (real) vector field having no periodic orbit.” Former results of F. W. Wilson and P. A. Schweitzer as well as some examples and problems are also analyzed.
For the entire collection see [Zbl 0811.00012].

Reviewer: M.A.Teixeira (Campinas)

MSC:

57R25

Vector fields, frame fields in differential topology

Keywords:

Seifert conjecture; vector field; periodic orbit