Counterexamples to the Seifert conjecture

  • Krystyna Kuperberg


Since H. Seifert proved in 1950 the existence of a periodic orbit for a vector field on the 3-dimensional sphere which forms small angles with the fibers of the Hopf fibration, several examples of aperiodic vector fields on have been produced as well as results showing that in some situations a compact orbit must exist. This paper surveys presently known types of vector fields without periodic orbits on and on other manifolds.