## About this book

### Introduction

"*This textbook, probably the best introduction to differential geometry to be published since Eisenhart's, greatly benefits from the author's knowledge of what to avoid, something that a beginner is likely to miss. The presentation is smooth, the choice of topics optimal, and the book can be profitably used for self teaching."* --- **The Bulletin of Mathematical Books (review of 1st edition)**

"*A thorough, modern, and lucid treatment of the differential topology, geometry, and global analysis needed to begin advanced study of research in these areas*." --- **Choice (review of 1st edition)**

"*Probably the most outstanding novelty...is the appropriate selection of topics*." --- **Mathematical Reviews (review of 1st edition)**

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. *Differentiable Manifolds* is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field.

The themes of linearization, (re) integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further (optional) development of Lie theory than is customary in textbooks at this level. New to this edition is a detailed treatment of covering spaces and the fundamental group.

Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.

### Keywords

### Bibliographic information

- DOI https://doi.org/10.1007/978-1-4757-2284-0
- Copyright Information Birkhäuser Boston 1993
- Publisher Name Birkhäuser, Boston, MA
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4757-2286-4
- Online ISBN 978-1-4757-2284-0
- Buy this book on publisher's site