Paul A. Schweitzer
Paul A. Schweitzer | |
|---|---|
| Born | Paul Alexander Schweitzer July 21, 1937 Yonkers, New York, U.S. |
| Nationality | American |
| Alma mater | College of the Holy Cross (BS) Princeton University (PhD) Weston College (PhL, BDiv) |
| Scientific career | |
| Fields | Topology |
| Institutions | Institute for Advanced Study Pontifical Catholic University of Rio de Janeiro |
| Thesis | Secondary cohomology operations induced by the diagonal mapping (1962) |
| Doctoral advisor | Norman Steenrod |
| Doctoral students | Suely Druck |
Paul Alexander Schweitzer SJ (born July 21, 1937) is an American mathematician specializing in differential topology, geometric topology, and algebraic topology.
Schweitzer 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.