## Topology from the Differentiable ViewpointThis 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. |

### What people are saying - Write a review

Full of rubbish. Milnor does not know how to impart mathematical knowledge to a fresher having good prerequisites. Perhaps he does not like, others know the subject otherwise his importance woud be diminished.

Este librito es realmente hermoso, es claro, conciso, y contiene muy buenos ejemplos. Solo se necesitan conocimientos básicos de cálculo y topología para leerlo.

This book is simply beautifull, is clear, concise, is full of interesting examples. You need as background only basic knowleges of calculus and point set topology.

### Contents

Smooth manifolds and smooth maps | 1 |

The theorem of Sard and Brown | 10 |

Proof of Sards theorem | 16 |

Oriented manifolds | 26 |

Vector fields and the Euler number | 32 |

Framed cobordism the Pontryagin construction | 42 |

Exercises | 52 |