Novikov, S.P. (Ed) - Topology I. General Survey (Encyclopedia Math.Sci., Springer)(T)(321s).pdf

文档介绍：S. P. Novikov (Ed.)
Topology I
General Survey
With 78 Figures
Springer
Encyclopaedia of
Mathematical Sciences
Volume 12
Editor-in-Chief: RX Gamkrelidze
Topology
Sergei P. Novikov
Translated from the Russian
by Boris Botvinnik and Robert Burns
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Introduction to the English Translation . . . . . . . . . . . . . . . . . . . . 5
Chapter 1. The Simplest Topological Properties . . . . . . . . . . . . . . . . . . . 5
Chapter 2. Topological Spaces. Fibrations. Homotopies ............. 15
$1. Observations from general topology. Terminology ............... 15
$2. Homotopies. Homotopy type ................................. 18
$3. Covering homotopies. Fibrations ............................. 19
54. Homotopy groups and fibrations. Exact sequences. Examples .... 23
Chapter 3. plexes and plexes. Homology and
Cohomology. Their Relation to Homotopy Theory. Obstructions . . . . . 40
$1. plexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
$2. The homology and cohomology groups. Poincare duality . . . . . . . . 47
83. Relative homology. The exact sequence of a pair. Axioms for
homology theory. plexes . . . . . . . . . . . . . . . . . . . . . . 57
$4. plexes and other homology theories. Singular
homology. Coverings and sheaves. The exact sequence of sheaves
and cohomology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
$5. Homology theory of non-simply-connected spaces. Complexes
of modules. Reidemeister torsion. Simple homotopy type . . . . . . . . 70
2 Contents
93. Simplicial and cell bundles with a structure group. Obstructions.
Universal objects: universal fiber bundles and the universal
property of Eilenberg-plexes. Cohomology
operations. The Steenrod algebra. The Adams spectral sequence 79
§7. The