Differential Topology [electronic resource]

Differential Topology
Author: Morris W. Hirsch
Published by Springer New York
ISBN: 978-1-4684-9451-8
DOI: 10.1007/978-1-4684-9449-5
Introduction -- Manifolds and Maps -- Function Spaces -- Transversality -- Vector Bundles and Tubular Neighborhoods -- Degrees, Intersection Numbers and the Euler Characteristic -- Morse Theory -- Corbodism -- Isotopy -- Surfaces -- Bibliography -- Appendix -- Index
This book gives the reader a thorough knowledge of the basic topological ideas necessary for studying differential manifolds. These topics include immersions and imbeddings, approach techniques, and the Morse classification of surfaces and their cobordism. The author keeps the mathematical prerequisites to a minimum; this and the emphasis on the geometric and intuitive aspects of the subject make the book an excellent and useful introduction for the student. There are numerous excercises on many different levels ranging from practical applications of the theorems to significant further development of the theory and including some open research problems