Topology From The Differentiable Viewpoint: 21 - Brossura

John Milnor

Brossura

ISBN 10: 0691048339 ISBN 13: 9780691048338

Casa editrice: New Publisher, 2021

Riassunto

This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

Su questo libro

Contenuti:

	Preface
1	Smooth manifolds and smooth maps	1
	Tangent spaces and derivatives	2
	Regular values	7
	The fundamental theorem of algebra	8
2	The theorem of Sard and Brown	10
	Manifolds with boundary	12
	The Brouwer fixed point theorem	13
3	Proof of Sard's theorem	16
4	The degree modulo 2 of a mapping	20
	Smooth homotopy and smooth isotopy	20
5	Oriented manifolds	26
	The Brouwer degree	27
6	Vector fields and the Euler number	32
7	Framed cobordism; the Pontryagin construction	42
	The Hopf theorem	50
8	Exercises	52
App	Classifying 1-manifolds	55
	Bibliography	59
	Index	63

Product Description:

Book by John Willard Milnor

Su questa edizione

• Editore: New Publisher
• Data di pubblicazione: 2021
• ISBN 10: 0691048339
• ISBN 13: 9780691048338
• Rilegatura: Copertina flessibile
• Numero di pagine: 64