Algebraic TopologySpringer New York, 1981 - 528 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. |
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Set theory | 1 |
Modules | 7 |
Categories | 14 |
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Expressions et termes fréquents
abelian groups acyclic algebra base point base space bundle chain complex chain equivalence chain map cochain coefficients commutative diagram compact composite continuous map COROLLARY Let corresponding covariant functor covering projection CW complex defined deformation retract denoted element epimorphism fiber fibration fibration with unique finite follows from theorem fundamental group Given Hausdorff space homology theory homomorphism homotopy classes homotopy groups homotopy type Hq(C inclusion map induces an isomorphism inverse K₁ K₂ LEMMA Let Let f locally path connected map f map pair monomorphism morphisms n-manifold neighborhood open covering orientable path component path-connected space pointed space presheaf PROOF Let prove q-simplex relative CW complex short exact sequence simplex simplicial approximation simplicial complex simplicial map simply connected singular singular homology spectral sequence subcomplex subspace THEOREM Let topological space unique path lifting vertex vertices X,xo Y,yo