Topology II

• Part I. Introduction to Homotopy Theory by O.Ya.Viro and D.B.Fuchs: 1. Basic Concepts.- 2. Bundle Techniques.- 3. Cellular Techniques.- 4. The Simplest Calculations.- Part II. Homology and Cohomology by O.Ya. Viro and D.B.Fuchs: 1. Additive Theory.- 2. Multiplicative Theory.- 3. Obstructions, Characteristic Classes and Cohomology Operations.- References.- Part III. Classical Manifolds by D.B.Fuchs: Introduction.- 1. Spheres.- 2. Lie Groups and Stiefel Manifolds.- 3. Grassman Manifolds and Spaces.- 4. Some Other Important Homogeneous Spaces.- 5. Some Manifolds of Low Dimension.- References.

From the reviews: "[...] The presentation of notions and results in all three chapters is really very nice. The first two chapters contain quite detailed exposition, while the third chapter has a more encyclopedia like character. This means that the first two chapters can also serve very well as a textbook. I would even recommend them for this purpose, because the presentation is on one hand a detailed one (as already mentioned), and on the other hand it is not too long. The choice of material is very good, the text is saturated with many examples, and we find here information about further developments and recommendations for further study. [...]. The last chapter contains information about the topology of classical manifolds, and I do not think that information of this type, in such a compact form and to such an extent, can be found elsewhere. Generally, the whole volume makes a very good impression, and I would say that it is very clearly written." European Mathematical Society Newsletter, Sept. 2004, p. 47 "... A good survey must include enough details to represent an area accurately and exclude enough details to remain accessible to readers. A third desirable ingredient in a survey of an area that already contains many good books is that it understand its place among books around it. This clearly written book on algebraic topology possesses each of these three ingredients. ..." Paul Norbury, Australian Math.Society GAZETTE, Volume 32, Issue1, 2005 "A good survey must include enough details to represent an area accurately and exclude enough details to remain accessible to readers. A third desirable ingredient in a survey of an area that already contains many good books is that it understand its place among books around it. This clearly written book on algebraic topology possesses each of these three ingredients. ... It is ideal as a good reference manual if you know what you are looking for." (Paul Norbury, The Australian Mathematical Society Gazette, Vol. 32 (1), 2005) "The presentation of notions and results in all three chapters is really very nice. ... The choice of material is very good, the text is saturated with many examples, and we find here information about further developments and recommendations for further study. ... I do not think that information of this type, in such a compact form and to such an extent, can be found elsewhere. Generally, the whole volume makes a very good impression, and I would say that it is very clearly written." (EMS - European Mathematical Society Newsletter, September, 2004)