Manifolds, Transversality & de Rham Cohomology by Peter Petersen
Manifolds, Transversality & de Rham Cohomology - Table of Contents
1. Manifolds and Smooth Maps
2. Tangent Spaces and Differentials of Maps
3. Global Theory of Smooth Maps
4. Lie Groups
5. Transversality and Incidence Theory
6. Basic Tensor Analysis
7. Basic Cohomology Theory
8. Intersection Theory Revisited
9. Characteristic Classes
What You Will Learn in Manifolds, Transversality & de Rham Cohomology
"Manifolds, Transversality and de Rham Cohomology" by Peter Petersen is a comprehensive introduction to "smooth manifolds", "transversality", and "de Rham cohomology". The book provides a clear and structured approach to differential geometry and topology, presenting foundational concepts like tangent spaces, vector bundles, and smooth maps in an accessible manner. It emphasizes understanding geometric structures and their relationships through rigorous yet intuitive explanations.
A key feature of the book is its treatment of "transversality", which studies how subspaces intersect in general position. Petersen explores applications such as intersection theory, degree theory, and fixed point results, illustrating how transversality provides powerful tools to analyze the geometry and topology of manifolds. This approach helps readers develop both conceptual and technical understanding of differential topology.
The book also introduces "de Rham cohomology", a method for computing topological invariants using differential forms. It connects these ideas to intersection numbers, Euler characteristics, and other geometric invariants, demonstrating the deep interplay between algebra, topology, and geometry. Ideal for advanced students and researchers, the text bridges fundamental theory with current mathematical methods, making it an essential resource for studying modern "geometry" and "topology".
Book Details & Specifications
Title:
Manifolds, Transversality & de Rham Cohomology by Peter Petersen
Publisher:
University of California
Year:
2018
Pages:
183
Type:
PDF
Language:
English
ISBN-10 #:
0821848151
ISBN-13 #:
978-0821848159
License:
University Educational Resource
Amazon:
Amazon
About the Author: Peter Petersen
The author Peter Petersen
is an "American mathematician" and Distinguished Professor at "UCLA", is known for his work in "Riemannian geometry" and curvature theory. His research and textbooks emphasize both rigorous mathematical foundations and geometric intuition, making complex concepts accessible and offering a solid reference for modern studies in topology and geometry. The book covers essential topics such as "transversality", "de Rham cohomology", and the structure of smooth manifolds, providing clear explanations for graduate students and researchers exploring geometric analysis.
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