Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three volumes of Modern Geometry - Methods and Applications contain a concrete exposition of these methods together with their main applications in mathematics and physics. This third volume, presented in highly accessible languages, concentrates in homology theory. It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto. Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text.
Book News Annotation:
Translated from the Russian edition of 1979, the authors presume their readers to be familiar with the contents of part II of their Modern geometry. The three chapters of the present volume bear these titles: Homology and cohomology: computational recipes, Critical points of smooth functions and homology theory, Cobordisms and smooth structures. Appendices treat an analog of Morse theory for many- valued functions, certain properties of Poisson brackets, and some some aspects of Plateau's problem. This is, in short, carefully developed advanced material, written with some sensitivity to the rapidly expanding practical needs of theoretical physicists of a certain breed. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
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