Fuchs D. Topology II. Homotopy and Homology. Classical Manifolds 2010 torrent

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Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.
Introduction to Homotopy Theory
Basic Concepts
Terminology and Notations
Homotopy
Homotopy Groups
Bundle Techniques
Bundles
Bundles and Homotopy Groups
The Theory of Coverings
Cellular Techniques
Cellular Spaces
Simplicial Spaces
Cellular Approximation of Maps and Spaces
The Simplest Calculations
The Homotopy Groups of Spheres and Classical Manifolds
Application of Cellular Techniques
Appendix
Homology and Cohomology
Additive Theory
Algebraic Preparation
General singular homology theory
Homology of cellular spaces
Homology and homotopy
Homology and fixed points
Other homology and cohomology theories
Multiplicative theory
Products
ogy and manifolds
Obstructions, characteristic classes and cohomology operations
Obstructions
Characteristic classes of vector bundles
Steenrod squares
Classical Manifolds
Spheres
Homotopy Groups
Differential Structures
Appendix
Lie Groups and Stiefel Manifolds
Lie Groups: Geometric Information
Lie Groups: Homological Information
Stiefel Manifolds
Grassmann Manifolds and Spaces
Geometric Information
Homology Information
Some Other Important Homogeneous Spaces
Flag Manifolds
The Manifold U(n)/SO(n) and U(n)/O(n)
The Manifolds SO(2n)/U(n) and U(2n)/Sp(n)
Some Manifolds of Low Dimension
Closed Surfaces
Some Three-dimensional Manifolds
Some Four-dimensional Manifolds