《约翰.米尔诺（John.Milnor）著作》(John Mlinor's book)(John W. Milnor)影印版[DJVU]

中文名: 约翰.米尔诺（John.Milnor）著作

原名: John Mlinor's book

作者: John W. Milnor

译者: 无

图书分类: 教育/科技

资源格式: DJVU

版本: 影印版

出版社: Princeton University Press, and so on

书号: 0-691-08008-9

发行时间: 1963年

地区: 美国

语言: 英文

简介:

约翰米尔诺应该是个公认的牛人了。菲尔兹和沃尔夫奖双料得主，学术上的没的说。更难得的是他写的教材基本上都成了名著。上学那会儿，N多老师推荐他的书，清晰流畅是他书的特点。或许这些书稍微有点年代久远，但是应该还是非常值得一看的。

这里收集一些Milnor的论文和书。其中一篇论文是他的那个成名作“7维怪球”，另一篇是一个关于布罗威尔不动点定理的解析证明。书籍包括著名那本《莫尔斯理论》，《从微分观点看拓扑》等等。最后还加了一本庆祝他60岁生日的文集。

这个资料比较专业，非科普。

--------------维基百科上Milnor的生平----------------------

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. He won the Fields Medal in 1962 and Wolf Prize in 1989. As of 2005, Milnor is a distinguished professor at the State University of New York at Stony Brook. His wife, Dusa McDuff, is a professor of mathematics at Barnard College.

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 was an editor of the Annals of Mathematics for a number of years after 1962.

His students have included Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. 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. Egbert Brieskorn found simple algebraic equations for 28 complex hypersurfaces in complex 5-space such that their intersection with a small sphere of dimension 9 around a singular point is diffeomorphic to these exotic spheres. Consequently Milnor worked on the topology of isolated singular points of complex hypersurfaces in general, developing the theory of the Milnor fibration whose fibre has the homotopy type of a bouquet of μ spheres where μ is known as the Milnor number. Milnor's 1968 book on his theory inspired the growth of a huge and rich research area which continues to develop to this day.