Paul A. Schweitzer

Paul A. Schweitzer
Born
Paul Alexander Schweitzer

(1937-07-21) July 21, 1937 (age 87)
Yonkers, New York, U.S.
NationalityAmerican
Alma materCollege of the Holy Cross (BS)
Princeton University (PhD)
Weston College (PhL, BDiv)
Scientific career
FieldsTopology
InstitutionsInstitute for Advanced Study
Pontifical Catholic University of Rio de Janeiro
Thesis Secondary cohomology operations induced by the diagonal mapping  (1962)
Doctoral advisorNorman Steenrod
Doctoral studentsSuely Druck

Paul Alexander Schweitzer SJ (born July 21, 1937) is an American mathematician specializing in differential topology, geometric topology, and algebraic topology.[1]

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.[2] 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.[3]

  1. ^ Saldanha, Nicolau C., ed. (2009). Foliations, geometry, and topology : Paul Schweitzer festschrift: conference in honor of the 70th birthday of Paul Schweitzer, S.J., August 6–10, 2007, PUC-Rio, Rio de Janeiro, Brazil. American Mathematical Society. ISBN 9780821846285.
  2. ^ Schweitzer, P. A. (1974). "Counterexamples to the Seifert conjecture and opening closed leaves of foliations". Annals of Mathematics. 100 (2): 386–400. doi:10.2307/1971077. JSTOR 1971077.
  3. ^ Schweitzer, Paul A. (1995). "Codimension one foliations without compact leaves". Commentarii Mathematici Helvetici. 70 (1): 171–209. doi:10.1007/BF02566004. S2CID 120853552.