Differential Topology

Graduate Texts in Mathematics #33

by Morris W. Hirsch

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." ―MATHEMATICAL REVIEWS

Genres: Mathematics

232 pages, Hardcover

First published July 1, 1976

Reviews

[Frau · Rating 2 out of 5]

Fine for a textbook on differential topology. Given its date of publication there is some outdated information such as some statements on the Poincare conjecture that no longer apply to the modern day. The aforementioned example can be found on page 2. Such an immediate inaccuracy sums up some of the other things you can find later in the book.

Unfortunately, not many ideal (accessible) alternatives exist. Additional research into anything you find interesting will likely un-disinform you most cases, so exercise caution. Most of the problems found here apply similarly to Victor W. Guillemin's 'Differential Topology' anyway. This part of mathematics is in a difficult position as while it has many advances in research regularly, it doesn't get many textbooks focused on it. A modern textbook based generally on topology as a whole won't help rectify this outdated information as already having read those is likely what would lead one to read a textbook like this in the first place.

In conclusion, someone new to this field of research won't gain very much knowledge from this book that they can trust as being accurate. However, the book still has interesting parts, and the mistakes can be amusing at times.

[Ezra · Rating 5 out of 5]

One of the only books that states and proves the most general versions of many foundational results needed for geometric topology.