Includes bibliographies and indexes.

Contents: Homology and Cohomology; Computational Recipes.- Critical Points of Smooth Functions and Homology Theory.- Cobordisms and Smooth Structures.- Bibliography.- Appendix 1, 2.- Index

Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have assumed 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 on 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.