This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.
Contents:
- Basic Concepts:
- Manifolds as Subsets of Euclidean Space
- Abstract Manifolds
- Manifolds with Boundary
- Partitions of Unity
- The Tangent Space
- The Differential
- Immersions, Submersions, and Submanifolds
- Embeddings and Whitney's Theorem
- Foliations
- Quotients
- Lie Theory:
- Vector Fields and Flows
- Lie Bracket and Lie Derivative
- Distributions and the Frobenius Theorem
- Lie Groups and Lie Algebras
- Integrations of Lie Algebras
- The Exponential Map
- Groups of Transformations
- Differential Forms:
- Differential Forms and Tensor Fields
- Volume Forms and Orientation
- Cartan Calculus
- Integration on Manifolds
- de Rham Cohomology
- The de Rham Theorem
- Homotopy Invariance and Mayer–Vietoris Sequence
- Computations in Cohomology and Applications
- The Degree and the Index
- Fiber Bundles:
- Vector Bundles
- The Thom Class and the Euler Class
- Pullbacks of Vector Bundles
- The Classification of Vector Bundles
- Connections and Parallel Transport
- Curvature and Holonomy
- The Chern–Weil Homomorphism
- Characteristic Classes
- Fiber Bundles
- Principal Fiber Bundles
Readership: For advanced undergraduate and beginning graduate level courses in Mathematics/Physics on Differential Geometry.
Key Features:
- The book is much more concise than other textbooks in differential geometry, but it still gives a clear, detailed and careful discussion of the most important topics necessary to grasp the subject
- Some topics, such as the Godement criteria for quotients, are usually not discussed in other textbooks
- Each lecture ends with a list of homework problems, carefully chosen to complete the topics covered in the lecture
This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.
Contents:
- Basic Concepts:
- Manifolds as Subsets of Euclidean Space
- Abstract Manifolds
- Manifolds with Boundary
- Partitions of Unity
- The Tangent Space
- The Differential
- Immersions, Submersions, and Submanifolds
- Embeddings and Whitney's Theorem
- Foliations
- Quotients
- Lie Theory:
- Vector Fields and Flows
- Lie Bracket and Lie Derivative
- Distributions and the Frobenius Theorem
- Lie Groups and Lie Algebras
- Integrations of Lie Algebras
- The Exponential Map
- Groups of Transformations
- Differential Forms:
- Differential Forms and Tensor Fields
- Volume Forms and Orientation
- Cartan Calculus
- Integration on Manifolds
- de Rham Cohomology
- The de Rham Theorem
- Homotopy Invariance and Mayer–Vietoris Sequence
- Computations in Cohomology and Applications
- The Degree and the Index
- Fiber Bundles:
- Vector Bundles
- The Thom Class and the Euler Class
- Pullbacks of Vector Bundles
- The Classification of Vector Bundles
- Connections and Parallel Transport
- Curvature and Holonomy
- The Chern–Weil Homomorphism
- Characteristic Classes
- Fiber Bundles
- Principal Fiber Bundles
Readership: For advanced undergraduate and beginning graduate level courses in Mathematics/Physics on Differential Geometry.
Key Features:
- The book is much more concise than other textbooks in differential geometry, but it still gives a clear, detailed and careful discussion of the most important topics necessary to grasp the subject
- Some topics, such as the Godement criteria for quotients, are usually not discussed in other textbooks
- Each lecture ends with a list of homework problems, carefully chosen to complete the topics covered in the lecture
LECTURES ON DIFFERENTIAL GEOMETRY
420
LECTURES ON DIFFERENTIAL GEOMETRY
420Related collections and offers
Product Details
| ISBN-13: | 9789811252662 |
|---|---|
| Publisher: | WSPC |
| Publication date: | 09/03/2024 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 420 |
| File size: | 27 MB |
| Note: | This product may take a few minutes to download. |