Algebraic TopologyCambridge University Press, 2002 - 544 pages In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers. |
Table des matières
II | ix |
III | 1 |
IV | 4 |
V | 6 |
VI | 10 |
VII | 17 |
IX | 21 |
X | 25 |
XLIX | 229 |
L | 235 |
LI | 245 |
LII | 248 |
LIII | 257 |
LIV | 264 |
LV | 277 |
LVI | 288 |
XI | 30 |
XII | 36 |
XIII | 37 |
XIV | 39 |
XV | 46 |
XVI | 52 |
XVII | 56 |
XVIII | 59 |
XIX | 66 |
XX | 79 |
XXI | 83 |
XXII | 93 |
XXIII | 98 |
XXIV | 100 |
XXV | 104 |
XXVI | 106 |
XXVII | 109 |
XXVIII | 124 |
XXIX | 130 |
XXXI | 133 |
XXXII | 145 |
XXXIII | 149 |
XXXIV | 156 |
XXXV | 158 |
XXXVI | 162 |
XXXVII | 165 |
XXXVIII | 173 |
XXXIX | 181 |
XLI | 186 |
XLIII | 193 |
XLIV | 202 |
XLV | 207 |
XLVI | 214 |
XLVII | 220 |
XLVIII | 226 |
LVII | 299 |
LVIII | 307 |
LIX | 317 |
LX | 323 |
LXI | 333 |
LXII | 335 |
LXIII | 336 |
LXIV | 342 |
LXV | 344 |
LXVI | 348 |
LXVII | 356 |
LXVIII | 362 |
LXIX | 371 |
LXX | 380 |
LXXI | 389 |
LXXII | 401 |
LXXIII | 406 |
LXXIV | 411 |
LXXV | 417 |
LXXVI | 423 |
LXXVII | 425 |
LXXVIII | 427 |
LXXIX | 444 |
LXXX | 448 |
LXXXI | 452 |
LXXXII | 456 |
LXXXIII | 462 |
LXXXIV | 466 |
LXXXV | 471 |
LXXXVI | 483 |
LXXXVII | 515 |
LXXXVIII | 529 |
535 | |
Expressions et termes fréquents
A-complex abelian groups algebra attaching basepoint boundary maps cell chain complex chain map circle cochain coefficients cohomology commutative diagram compact composition construction covering space cross product cup product CW complex CW structure defined deformation retracts dimension edges element example fiber bundle fibration finite formula functor fundamental group graph group G H-space H₁ H₂ hence homology groups homology theory homomorphism homotopy classes homotopy equivalence homotopy type Hopf identity implies inclusion induces an isomorphism injective isomorphism Lemma lift long exact sequence loop mapping cylinder multiplication n-cells neighborhood nontrivial nonzero obtained orientable pair path path-connected polynomial Proof Proposition quotient map restriction ring short exact sequence simplicial simply-connected singular SO(n subcomplex subgroup subspace summand surjective suspension theorem topology torus trivial union universal cover v₁ vector vertex vertices wedge sum X₁ Z₂ zero π₁