Based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics, this volume consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and Andr Weil, as well as a proof of the Gauss-Bonnet-Chern theorem based on the Mathai-Quillen construction of Thom forms; the second part presents analytic proofs of the Poincar-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.
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Editorial Reviews
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"The book gives an excellent introduction to these analytic techniques" -- Mathematical Reviews, 2002
This book is noteworthy for its combination of brevity, clarity, accessibility, and depth. -- Mathematics Abstracts --This text refers to the Hardcover edition.
This book is noteworthy for its combination of brevity, clarity, accessibility, and depth. -- Mathematics Abstracts --This text refers to the Hardcover edition.
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Readership: Graduate students and researchers in differential geometry, topology and mathematical physics
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First Sentence:
The theory of characteristic classes of vector bundles over smooth manifolds plays important roles in topology and geometry. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Berlin-Heidelberg-New York, Princeton Univ, Algebraic Topology, Wissenschften Vol, World Scientific New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The theory of characteristic classes of vector bundles over smooth manifolds plays important roles in topology and geometry. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Berlin-Heidelberg-New York, Princeton Univ, Algebraic Topology, Wissenschften Vol, World Scientific New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
See all 11 books this book cites
4
books
cite this book:
- Differential Forms in Algebraic Topology (Graduate Texts in Mathematics) by Raoul Bott on page 27, page 54, and page 74
- Lectures on Differential Geometry (Series on University Mathematics) by Shiing-Shen Chern on page 27, and page 54
- Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) (v. 94) by Frank W. Warner on page 74, and page 103
- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern on page 27, and page 54
- The Topology of Fibre Bundles. (PMS-14) by Norman Steenrod on page 27, and page 115
See all 11 books this book cites
- Contemporary Trends in Algebraic Geometry and Algebraic Topology by Shiing-Shen Chern in Front Matter
- Minimal Submanifolds and Related Topics (Nankai Tracts in Mathematics) by Yuanlong Xin in Front Matter
- Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture by Wu Yi Hsiang in Front Matter
- Iterated Integrals and Cycles on Algebraic Maniforlds (Nankai Tracts in Mathematics, Vol. 7) by Bruno Harris in Front Matter
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