High Quality Content by WIKIPEDIA articles! In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit. It is named after Herbert Seifert. In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non-existence as a conjecture. He also established the conjecture for perturbations of the Hopf fibration. The conjecture was disproven in 1974 by Paul Schweitzer, who exhibited a C1 counterexample. Schweitzer's construction was then modified by Jenny Harrison in 1988 to make a C2 + ? counterexample for some ? > 0.

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