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About: Paul A. Schweitzer     Goto   Sponge   NotDistinct   Permalink

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Paul Alexander Schweitzer, S. J., (born 21 July 1937, Yonkers, New York) is an American mathematician, specializing in differential topology, geometric topology, and algebraic topology. He has done research on foliations, knot theory, and 3-manifolds. In 1974 he found a counterexample to the Seifert conjecture that every non-vanishing vector field on the 3-sphere has a closed integral curve. In 1995 he demonstrated that Sergei Novikov's compact leaf theorem cannot be generalized to manifolds with dimension greater than 3. Specifically, Schweitzer proved that a smooth, compact, connected manifold with Euler characteristic zero and dimension > 3 has a C1 codimension-one foliation that has no compact leaf.