Elements of homology theory. Prasolov. (2004)

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This book is a direct continuation of the book "Elements of combinatorial and differential topology." It begins with the definition of simplicial homology and cohomology; Many examples of their calculation and their application. Then discusses the multiplication of the Kolmogorov-Alexander on cohomology. Much of the book is devoted to various applications (simplicial) homology and cohomology. Many of them are connected with the theory of constraints. One such example are the characteristic classes of vector bundles. Singular homology and cohomology are determined in the second half of the book. Then considered another approach to the construction of the theory of cohomology - cohomology Cech and closely related de Rham cohomology with them. The book concludes with the various applications of homology theory in the topology of manifolds. The book contains a lot of problems (with solutions) and exercises for
independent decision. For senior students and graduate students of mathematical and physical disciplines; for scientists.

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