Topology from the Differentiable Viewpoint by Milnor

[micromass]

• Author: John Milnor
• Title: Topology from the Differentiable Viewpoint
• Amazon Link: https://www.amazon.com/dp/0691048339/?tag=pfamazon01-20
• Prerequisities:
• Level: Undergrad

Table of Contents:

[LIST]
[*] Preface
[*] Smooth manifolds and smooth maps
[*] Tangent spaces and derivatives
[*] Regular values
[*] The fundamental theorem of algebra
[*] The theorem of Sard and Brown
[*] Manifolds with boundary
[*] The Brouwer fixed point theorem
[*] Proof of Sard's theorem
[*] The degree modulo 2 of a mapping
[*] Smooth homotopy and smooth isotopy
[*] Oriented manifolds
[*] The Brouwer degree
[*] Vector fields and the Euler number
[*] Framed cobordism; the Pontryagin construction
[*] The Hopf theorem
[*] Exercises
[*] Appendix: Classifying 1-manifolds
[*] Bibliography
[*] Index
[/LIST]

 

[mathwonk]

It is hard to imagine a book which will teach more in fewer pages than this one. A significant expansion of much of this material is in the book by Guillemin and Pollack.

 

[Greg Bernhardt]

mathwonk, your library must rival the great Alexandria's :)

 

[mathwonk]

Unfortunately i gave some volumes away when i moved out of my office. But my collection's strong representation in this sample is skewed because these books on this list are of such high quality!

(It is also partly because I am always trying to find books aimed at beginners and students from which I myself can learn new topics. Some of my friends have much larger collections of more advanced and specialized books.)

In fact my copy of Milnor's book which I bought in about 1966, was autographed by him in 1997 on the occasion of his delivering the Cantrell lectures at UGA.

http://www.math.uga.edu/seminars_conferences/milnor-lectures.htm