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Topology II: Homotopy and Homology. Classical Manifolds
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Topology II: Homotopy and Homology. Classical Manifolds Hardcover - 2003

by V. a. Rokhlin (Editor); C. Shaddock (Translator); D. B. Fuchs


From the publisher

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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In addition to the standard set-theoretical terminology and notations, whose use is unambiguous, we shall use the following.

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  • Title Topology II: Homotopy and Homology. Classical Manifolds
  • Author V. a. Rokhlin (Editor); C. Shaddock (Translator); D. B. Fuchs
  • Binding Hardcover
  • Edition 1st
  • Pages 258
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Date 2003-10-27
  • Illustrated Yes
  • Features Illustrated, Maps
  • ISBN 9783540519966 / 3540519963
  • Weight 1.13 lbs (0.51 kg)
  • Dimensions 9.46 x 6.22 x 0.8 in (24.03 x 15.80 x 2.03 cm)
  • Dewey Decimal Code 514.2
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