Topology II

Homotopy and Homology. Classical Manifolds
1. Auflage. Softcover version of original hardcover Auflage 2004
ISBN: 978-3-642-08084-5
Verlag: Springer

Buch, Englisch, Band 24, 258 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Reihe: Encyclopaedia of Mathematical Sciences

to Homotopy Theory O. Ya. Viro, D. B. Fuchs Translated from the Russian by C. J. Shaddock Contents Chapter 1. Basic Concepts. 4 § 1. Terminology and Notations. 4 1. 1. Set Theory. 4 1. 2. Logical Equivalence. 4 1. 3. Topological Spaces. 5 1. 4. Operations on Topological Spaces. 5 1. 5. Operations on Pointed Spaces. 8 §2. Homotopy. 10 2. 1. Homotopies. 10 2. 2. Paths. 10 2. 3. Homotopy as a Path. 11 2. 4. Homotopy Equivalence. 11 2. 5. Retractions. 11 2. 6. Deformation Retractions. 12 2. 7. Relative Homotopies. 13 2. 8. k-connectedness. 13 2. 9. Borsuk Pairs. 14 2. 10. CNRS Spaces. 15 2. 11. Homotopy Properties of Topological Constructions. 15 2. 12. Natural Group Structures on Sets of Homotopy Classes. 16 §3. Homotopy Groups. 20 3. 1. Absolute Homotopy Groups. 20 2 O. Ya. Viro, D. B. Fuchs 3. 2. Digression: Local Systems. 22 3. 3. Local Systems of Homotopy Groups of a Topological Space. 23 3. 4. Relative Homotopy Groups. 25 3. 5. The Homotopy Sequence of a Pair. 28 3. 6. Splitting. 31 3. 7. The Homotopy Sequence of a Triple. 32 Chapter 2. Bundle Techniques. 33 §4. Bundles. 33 4. 1. General Definitions. 33 4. 2. Locally Trivial Bundles. 34 4. 3. Serre Bundles. 36 4. 4. Bundles of Spaces of Maps. 37 §5. Bundles and Homotopy Groups. 38 5. 1. The Local System of Homotopy Groups of the Fibres of a Serre Bundle.

Zielgruppe

Research

Autoren/Hrsg.

Fuchs, D. B.

Viro, O. Ya.

Rokhlin, V.A.

Novikov, S. P.

Weitere Mitwirkende

Shaddock, C.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.