Author Description
Bundles, Connections, Metrics And Curvature Are The 'lingua Franca' Of Modern Differential Geometry And Theoretical Physics. This Book Will Supply A Graduate Student In Mathematics Or Theoretical Physics With The Fundamentals Of These Objects. Many Of The Tools Used In Differential Topology Are Introduced And The Basic Results About Differentiable Manifolds, Smooth Maps, Differential Forms, Vector Fields, Lie Groups, And Grassmanians Are All Presented Here. Other Material Covered Includes The Basic Theorems About Geodesics And Jacobi Fields, The Classification Theorem For Flat Connections, The Definition Of Characteristic Classes, And Also An Introduction To Complex And Kähler Geometry. Differential Geometry Uses Many Of The Classical Examples From, And Applications Of, The Subjects It Covers, In Particular Those Where Closed Form Expressions Are Available, To Bring Abstract Ideas To Life. Helpfully, Proofs Are Offered For Almost All Assertions Throughout. All Of The Introductory Material Is Presented In Full And This Is The Only Such Source With The Classical Examples Presented In Detail.
Menrva's Summary
THE THESIS
This text investigates the fundamental structures of differential geometry, specifically focusing on bundles, connections, metrics, and curvature as the primary language for modern mathematics and theoretical physics. Clifford Henry Taubes, a professor of mathematics at Harvard University, utilizes his extensive research background to provide a rigorous framework for graduate-level study. The book synthesizes core concepts of differentiable manifolds and topology to bridge the gap between abstract theory and concrete physical applications.
THE SCOPE MAP
What You Will Find
- Comprehensive coverage of differentiable manifolds, smooth maps, and differential forms.
- Detailed examination of Lie groups, Grassmanians, and characteristic classes.
- Theoretical foundations of geodesics, Jacobi fields, and Kähler geometry.
- Extensive use of classical examples with closed-form expressions to illustrate abstract concepts.
Scope Limits
- The text assumes a baseline of undergraduate mathematical maturity and does not provide remedial instruction in basic calculus or linear algebra.
- It focuses primarily on the geometric and topological aspects relevant to physics rather than exhaustive historical or philosophical context.
THE AUTHORITY PERSPECTIVE
Experts and graduate students frequently cite this work as a rigorous and self-contained resource for mastering the technical machinery of modern geometry. Readers often note the density of the prose, which is balanced by the inclusion of detailed proofs for nearly all presented assertions.
Page Count:
312
Publication Date:
2011-01-01
Publisher:
Oup Oxford
ISBN-10:
0191621226
ISBN-13:
9780191621222
Theoretical Physics
Mathematics
Academic Textbooks
Topology
Differential Geometry
Community Tags
Similar Books
