Sylvain Cappell

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Sylvain Edward Cappell (born September 10, 1946 in Brussels ) is an American mathematician who studies topology .

Sylvain Cappell (right) with Joachim Heinze (center) and Jakow Sinai (left)

Cappell came to New York City around 1950, where he attended the Bronx High School of Science . As a high school student, he won the Westinghouse talent competition with a math work. He studied at Columbia University with a bachelor's degree in 1966 and received his doctorate in 1969 from Princeton University under William Browder ( super-spinning and knot complements ). From 1969 he was at Princeton University, where he became Assistant Professor, and from 1974 Associate Professor and from 1978 Professor at the Courant Institute of Mathematical Sciences of New York University . He is a Silver Professor of Mathematics there.

He is known for his Codimension 1 splitting theorem in the higher-dimensional geometric topology (emerged from his dissertation) and for a number of results with Julius Shaneson, among other things, on the higher-dimensional knot theory. to the problem of topological similarity (after Georges de Rham ) and finally to geometric numbers of grid points with number theoretic applications.

His decomposition theorems deal with the question of when a decomposition of a manifold M into a connected sum of submanifolds N (with codimension 1) is homotopy-invariant. He showed that this is the case if the fundamental group of N Root completed (square root closed) is in the fundamental group of M. The obstruction for the homotopy-invariant decomposition lies in so-called UNil groups.

In 1970/71 he was visiting professor at Harvard University (and again at Harvard in 1981), in 1973 at IHES and in 1972 at the Weizmann Institute .

Shmuel Weinberger is one of his PhD students .

In 2012 he became a Fellow of the American Mathematical Society and in 2018 a member of the American Academy of Arts and Sciences . In 1989/90 he was a Guggenheim Fellow , 1966/67 Woodrow Wilson Fellow and 1971 to 1973 Sloan Research Fellow .

He is a US citizen. He has been married since 1966 and has four children.

Fonts

  • A splitting theorem for manifolds and surgery groups, Bulletin AMS, Volume 77, 1971, pp. 281-286
  • with Shaneson The codimension two placement problem and homology equivalent manifolds , Annals of Mathematics, Volume 99, 1974, pp. 277-348
  • with Shaneson Non-linear Similarity , Annals of Mathematics, Volume 113, 1981, pp. 315-355
  • with Shaneson There exists inequivalent knots with the same complement , Annals of Mathematics, Volume 103, 1976, pp. 349-353
  • with Shaneson, Mark Steinberger, James E. West Nonlinear conjugacy begins in dimension six , American Journal of Mathematics, Volume 111, 1989, p. 717

Web links

Individual evidence

  1. ↑ Life data according to American Men and Women of Science , Thomson Gale 2004
  2. ^ Mathematics Genealogy Project . Published in Topology of Manifolds, Proc. of the 1969 Georgia Conference , Markham Press 1971, pp. 358-383
  3. ↑ Cappell A splitting theorem for manifolds , Inventiones Mathematicae, Volume 33, 1975, pp. 69-170, online
  4. ↑ Together with Shaneson, he constructed examples of non-equivalent n-2-dimensional nodes whose complements are homeomorphic in n-dimensional space. This distinguishes higher-dimensional from 3-dimensional knot theory, because for n = 3, according to a Gordon-Luecke theorem, the equivalence of the knots already follows from the homeomorphism of knot complements.
  5. ↑ He assumed that topological similarity of representations of finite groups (the vector spaces of the representation are equivariant homeomorphic) leads to linear equivalence. Cappell and Shaneson proved that in less than six dimensions, but gave counterexamples in dimension 6
  6. ^ Cappell, Shaneson Some problems in number theory I. The circle problem , Arxiv, 2007 . In this they tighten an asymptotic assessment by Johannes van der Corput
  7. ↑ With is also g in the group
  8. ↑ Shmuel Weinberger's blog on the splitting theorem ( Memento from April 12, 2013 in the web archive archive.today )
  9. ↑ Book of Members 1780 – present, Chapter C. (PDF; 1.3 MB) In: American Academy of Arts and Sciences (amacad.org). Retrieved July 1, 2018 .
personal data
SURNAME Cappell, Sylvain
ALTERNATIVE NAMES Cappell, Sylvain Edward (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH September 10, 1946
PLACE OF BIRTH Brussels