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Topology 2 Homotopy And Homology, Classical Manifolds Book Freeshipping

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Topology 2 Homotopy and Homology, Classical Manifolds, by Novikov.S.P., English, Hardcover, 2009



Author Novikov.S.P.

Press Science Press

Isbn 703023510x/9787030235107

Publication Date Jan 2009

Pages 268

Size 16K

Edition First

Cover Hardcover

Language English

Page material gelatine plate paper

Product Description:

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an upto-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, Grassmannians and lowdimensional manifolds.

Their book will be used by graduate students and researchers in mathematics and mathematical physics.


Ⅰ. Introduction to Homotopy Theory

Chapter 1.Basic Concepts

1. Terminology and Notations

1.1. Set Theory

1.2. Logical Equivalence

1.3. Topological Spaces

1.4. Operations on Topological Spaces

1.5. Operations on Pointed Spaces

2. Homotopy

2.1. Homotopies

2.2. Paths

2.3. Homotopy as a Path

2.4. Homotopy Equivalence

2.5. Retractions

2.6. Deformation Retractions

2.7. Relative Homotopies

2.8. k-connectedness

2.9. Borsuk Pairs

2.10. CNRS Spaces

2.11. Homotopy Properties of Topological Constructions

2.12. Natural Group Structures on Sets of Homotopy Classes

3. Homotopy Groups

3.1. Absolute Homotopy Groups

3.2. Digression: Local Systems

3.3. Local Systems of Homotopy Groups of a Topological Space

3.4. Relative Homotopy Groups

3.5. The Homotopy Sequence of a Pair

3.6. Splitting

3.7. The Homotopy Sequence of a Triple

Chapter 2.Bundle Techniques

4. Bundles

4.1. General Definitions

4.2. Locally Trivial Bundles

4.3. Serre Bundles

4.4. Bundles of Spaces of Maps

5. Bundles and Homotopy Groups

5.1. The Local System of Homotopy Groups of the Fibres of a Serre Bundle

5.2. The Homotopy Sequence of a Serre Bundle

5.3. Important Special Cases

6. The Theory of Coverings

6.1. Coverings

6.2. The Group of a Covering

6.3. Hierarchies of Coverings

6.4. The Existence of Coverings

6.5. Automorphisms of a Coveting

6.6. Regular Coverings

6.7. Covering Maps

Chapter 3 Cellular Techniques

7. Cellular Spaces

7.1. Basic Concepts

7.2. Gluing of Cellular Spaces from Balls

7.3. Examples of Cellular Decompositions

7.4. Topological Properties of Cellular Spaces

7.5. Cellular Constructions

8. Simplicial Spaces

8.1. Basic Concepts

8.2. Simplicial Schemes

8.3. Simplicial Constructions

8.4. Stars, Links, Regular Neighbourhoods

8.5. Simplicial Approximation of a Continuous Map

9. Cellular Approximation of Maps and Spaces

9.1. Cellular Approximation of a Continuous Map

9.2. Cellular k-connected Pairs

9.3. Simplicial Approximation of Cellular Spaces

9.4. Weak Homotopy Equivalence

9.5. Cellular Approximation to Topological Spaces

9.6. The Covering Homotopy Theorem

Chapter 4 The Simplest Calculations

10. The Homotopy Groups of Spheres and Classical Manifolds

10.1. Suspension in the Homotopy Groups of Spheres

10.2. The Simplest Homotopy Groups of Spheres

10.3. The Composition Product

10.4. Homotopy Groups of Spheres

10.5. Homotopy Groups of Projective Spaces and Lens Spaces

10.6. Homotopy Groups of the Classical Groups

10.7. Homotopy Groups of Stiefel Manifolds and Spaces

10.8. Homotopy Groups of Grassmann Manifolds and Spaces

11. Application of Cellular Techniques

11.1. Homotopy Groups of a 1-dimensional Cellular Space

11.2. The Effect of Attaching Balls

11.3. The Fundamental Group of a Cellular Space

11.4. Homotopy Groups of Compact Surfaces

11.5. Homotopy Groups of Bouquets

11.6. Homotopy Groups of a k-connected Cellular Pair

11.7. Spaces with Given Homotopy Groups

12. Appendix

12.1. The Whitehead Product

12.2. The Homotopy Sequence of a Triad

12.3. Homotopy Excision, Quotient and Suspension Theorems

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