Customer Reviews

Differential Geometry: Cartan's Generalization of Klein's Erlangen Program (Graduate Texts in Mathematics)

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Sharpe's book is a detailed argument supporting the assertion that most of differential geometry can be considered the study of principal bundles and connections on them, disguised as an introductory differential geometry textbook.

Some standard introductory material (e.g. Stokes' theorem) is omitted, as Sharpe confesses in his preface, but otherwise this is a truly wonderful place to read about the central role of Lie groups, principal bundles, and connections in differential geometry. The theme is that what one can do for Lie groups, one can do fiberwise for principal bundles, to yield information about the base.

The informal style (just look at the table of contents) and wealth of classical examples make this book a pleasure to read. While its somewhat nonstandard approach and preference for classical terminology might confuse those who have never been introduced to the concepts, this is a perfect *second* place to read and marvel about differential geometry.

The book "Differential Geometry: Cartan's Generalization of Klein's Erlangen Program", purchase from NRVBOOKSPLUS via AMAZON.COM, exceed my expectations! It's completely new. It seems that no one has ever opened it. Also, I received the product very quickly. I'm so pleased with this purchase ande really recommend this seller.

I was fortunate enough to have Sharpe as my supervisor at University of Toronto just when his book was published. His highly abstract thinking is very impressive and I have enjoyed immensely his first chapter on differential topology, which is my specialized area. Though his book branches off into realms that don't particularly suit me, the beginnings of his book had given me great inspiration in my discipline in differential topology

This is definitely a graduate school text. Though I believe the text can be read by a eager undergraduate. The text is about Differential Geometry.

The subject matter demands that the reader read more than 1 book on the subject. This is a good introduction to a difficult but useful mathematical discipline.