Algebraic Topology

Couverture
Springer Science & Business Media, 1989 - 548 pages
Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, and topological manifolds. The remaining third of the book is devoted to Homotropy theory, covering basic facts about homotropy groups, applications to obstruction theory, and computations of homotropy groups of spheres. In the later parts, the main emphasis is on the application to geometry of the algebraic tools developed earlier.
 

Table des matières

Set theory
1
Modules
7
Categories
14
Homotopy
22
H spaces
33
Suspension
39
The fundamental groupoid
45
Exercises
56
Presheaves
323
Fine presheaves
329
Applications of the cohomology of presheaves
338
Characteristic classes
346
Exact sequences of sets of homotopy classes
364
Higher homotopy groups
371
Change of base points
379
The Hurewicz homomorphism
387

COVERING SPACES AND FIBRATIONS
64
Fiber bundles
95
Exercises
103
POLYHEDRA
114
HOMOLOGY
156
Exercises
205
Homology with coefficients
212
The universalcoefficient theorem for homology
219
The Künneth formula
227
Cohomology
236
Cup and cap products
248
Homology of fiber bundles
255
The cohomology algebra
263
The slant product
286
Duality in topological manifolds
293
The fundamental class of a manifold
299
The Alexander cohomology theory
306
Tautness and continuity
315
The Hurewicz isomorphism theorem
393
CW complexes
400
Homotopy functors
406
Weak homotopy type
412
Exercises
418
EilenbergMacLane spaces
424
Principal fibrations
432
Obstruction theory
445
The suspension map
452
SPECTRAL SEQUENCES AND HOMOTOPY
464
The spectral sequence of a fibration
473
Applications of the homology spectral sequence
481
Multiplicative properties of spectral sequences
490
Applications of the cohomology spectral sequence
498
Serre classes of abelian groups
504
Homotopy groups of spheres
512
Exercises
518
Droits d'auteur

Autres éditions - Tout afficher

Expressions et termes fréquents

Informations bibliographiques