This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back ground material. In order to emphasize the geometrical and intuitive aspects of differen tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems.
Differential Topology Free Download
April 9, 2022
You may also like
DISCRETE MATHEMATICS
Bird’s Higher Engineering Mathematics, 9th Edition By John Bird PDF
February 2, 2024
Higher Engineering Mathematics has helped thousands of students to succeed in their exams by developing problem-solving skills, It is supported by over 600...
DISCRETE MATHEMATICS
Complex Analytic Methods for Partial Differential Equations An Introductory Text by Heinrich G W Begehr PDF
January 13, 2024
This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and...
DISCRETE MATHEMATICS
Nonlinear Partial Differential Equations Asymptotic Behavior of Solutions and Self-Similar Solutions by Mi-Ho Giga PDF
January 13, 2024
The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear partial di...
Recent Posts
- Algebra 3 Homological Algebra and Its Applications by Ramji Lal PDF
- Heat Transfer Physics 2nd Edition By Massoud Kaviany PDF
- Lavin’s Radiography for Veterinary Technicians, 6th Edition by Marg Brown PDF
- Principles of Physics, 10th Edition by David Halliday PDF
- The Dog Behavior Problem Solver by Teoti Anderson PDF
Add Comment