- Series: Translations of Mathematical Monographs (Book 201)
- Paperback: 321 pages
- Publisher: American Mathematical Society (August 28, 2001)
- Language: English
- ISBN-10: 0821810456
- ISBN-13: 978-0821810453
- Product Dimensions: 1 x 5.5 x 8.5 inches
- Shipping Weight: 15.2 ounces
- Average Customer Review: 10 customer reviews
- Amazon Best Sellers Rank: #247,077 in Books (See Top 100 in Books)
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Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201)
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Top customer reviews
All in all, a wonderful book, but a word of caution, beware, reading to much of this book may make you fall in love with it!...so my advice, buy it you will be making a full worth investment, only take care of not making your girlfriend jealous by giving to much time to it despite of her!
For example, like Euler, we could count the number of holes in the surface and using this combinatorial method we are led to homology theory.
Or like Gauss, we could use a differentiation and integration to come up with the idea of curvature as an intrinsic feature of the surface.
Modern approaches use differential forms to represent homology and cohomoly groups.
The author also deals with fibre bundles demonstrating their importance in analyzing manifolds specifically how the number of fibre bundles possible with given Lie groups as structure groups over the manifold can be answered by characteristic classes such as the Chern and Pontrjagin classes. The use of differential forms is indispensible.
Perhaps the most satisfying aspect of this book is that it clarifies the notions of connection, connection form, curvature, curvature form for manifolds and fibre bundles.
There are plenty of exercises to boot.