JOHN MILNOR

'John Willard Milnor' (b. February 20, 1931 in Orange, New Jersey) is an American mathematician known for his work in differential topology, K-theory, and dynamical systems, and for his influential books, which are widely considered to be examples of fine mathematical writing. He won the Fields Medal in 1962. As of 2005, John Milnor is a distinguished professor at the State University of New York at Stony Brook. His wife, Dusa McDuff, is also a professor at Stony Brook.

Contents

Life

Work

See also

References

Articles

Books

External links

Life

As an undergraduate at Princeton University he was named a Putnam Fellow in 1949 and 1950 and also proved the Fary-Milnor theorem. He continued on to graduate school at Princeton and wrote his thesis, entitled ''isotopy of links'', which concerned link groups (a generalization of the classical knot group) and their associated link structure. His advisor was Ralph Fox. Upon completing his doctorate he went on to work at Princeton.
In 1962 Milnor was awarded the Fields Medal for his work in differential topology. He later went on to win the National Medal of Science (1967), the Leroy P Steele Prize for Seminal Contribution to Research (1982), the Wolf Prize in Mathematics (1989), and the Leroy P Steele Prize for Mathematical Exposition (2004). He has been editor of the Annals of Mathematics since 1962.
His students have included Tadatoshi Akiba, Jon Folkman, John Mather, Laurence Siebenmann, Jonathan Sondow, and Michael Spivak.

Work

His most celebrated single result is his proof of the existence of 7-dimensional spheres with nonstandard differential structure. Later with Michel Kervaire, he showed that the 7-sphere has 15 differentiable structures (28 if you consider orientation). An ''n''-sphere with nonstandard differential structure is called an exotic sphere, a term coined by Milnor.

See also

★ Fary-Milnor theorem

★ Milnor conjecture in algebraic K-theory

★ Milnor conjecture in knot theory

★ Milnor conjecture concerning manifolds with nonnegative Ricci curvature

★ Milnor map

★ Orbit portrait

References

Articles

★ [1] John Milnor, ''On manifolds homeomorphic to the 7-sphere'', Annals of Mathematics, 2nd Ser., '64' (1956), no. 2, 399 – 405

★ [2] Michel A. Kervaire, John W. Milnor, ''Groups of homotopy spheres. I.'', Annals of Mathematics, 2nd Ser., '77' (1963), no. 3, 504 – 537

Books

★ Morse theory, , John W., Milnor, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, NJ, 1963, ISBN 0-691-08008-9

★ Topology from the differentiable viewpoint, , John W., Milnor, Revised reprint of the 1965 original. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ, 1997, ISBN 0-691-04833-9

★ Characteristic classes, , John W., Milnor, Annals of Mathematics Studies, No. 76. Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1974, ISBN 0-691-08122-0

★ Milnor, John W., ''Lectures on the h-cobordism theorem'', notes by L. Siebenmann and J. Sondow, Princeton University Press, Princeton, NJ, 1965.

★ Singular points of complex hypersurfaces, , John W., Milnor, Annals of Mathematics Studies, No. 61. Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1968, ISBN 0-691-08065-8

★ ''Dynamics in one complex variable''

External links

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★ Home page at SUNYSB