An Introduction to Morse Theory:Ebook Free Download

Ebook Free Download | An Introduction to Morse Theory | Matsumoto's "Morse Theory" is one of few relatively recent treatments of finite-dimensional Morse theory, written at a level high enough to make it useful for advanced undergraduates or more likely graduate students, but with a slower pace than, say, one of Milnor's books.
Morse Theory, for the uninitiated, involves studying the behavior of functions on a smooth manifold near the critical points (of the functions) in order to deduce information about the topology of the manifold. It dates from the 1930s, but achieved its greatest results in the late '50s and early '60s with its application to the classification of manifolds via handlebody theory by Smale, Milnor, and Wallace, among others. Until now the standard treatises on the subject have been Milnor's Morse Theory and Lectures on the h-Cobordism Theorem, but the former focuses on differential geometric applications of the subject (as did Morse's classic Calculus of Variations in the Large) rather than topological ones, and the latter is OOP and hard to find. Moreover, both of these, while still relevant, are somewhat out of date, being over 40 years old and lacking any of the more recent developments in low dimensional topology, to say nothing of infinite-dimensional or complex Morse theory (which this book doesn't treat either). So certainly there is room for a new exposition of the subject, especially one geared toward students, and this one serves adequately enough.