A Concise Course in Algebraic TopologyAlgebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field. |
Contents
II | 7 |
III | 7 |
V | 8 |
VI | 10 |
VIII | 13 |
IX | 14 |
XI | 15 |
XII | 16 |
LXXVII | 121 |
LXXVIII | 122 |
LXXIX | 123 |
LXXX | 124 |
LXXXI | 126 |
LXXXII | 129 |
LXXXIII | 130 |
LXXXIV | 131 |
XIII | 17 |
XIV | 19 |
XV | 21 |
XVI | 22 |
XVIII | 23 |
XIX | 25 |
XX | 27 |
XXI | 28 |
XXII | 29 |
XXIII | 33 |
XXIV | 34 |
XXV | 35 |
XXVII | 37 |
XXVIII | 38 |
XXIX | 41 |
XXXI | 42 |
XXXII | 43 |
XXXIV | 44 |
XXXV | 47 |
XXXVI | 48 |
XXXVII | 49 |
XXXVIII | 50 |
XXXIX | 51 |
XL | 55 |
XLI | 56 |
XLII | 57 |
XLIII | 59 |
XLV | 61 |
XLVI | 63 |
XLVII | 64 |
XLIX | 66 |
L | 67 |
LI | 71 |
LII | 72 |
LIII | 73 |
LIV | 74 |
LV | 75 |
LVI | 76 |
LVII | 77 |
LVIII | 81 |
LIX | 83 |
LX | 84 |
LXI | 89 |
LXII | 90 |
LXIII | 91 |
LXIV | 93 |
LXV | 94 |
LXVI | 98 |
LXVII | 99 |
LXVIII | 101 |
LXIX | 105 |
LXX | 106 |
LXXI | 107 |
LXXII | 108 |
LXXIII | 110 |
LXXIV | 112 |
LXXV | 115 |
LXXVI | 117 |
LXXXV | 133 |
LXXXVII | 135 |
LXXXVIII | 136 |
LXXXIX | 137 |
XC | 138 |
XCI | 140 |
XCII | 143 |
XCIII | 144 |
XCIV | 145 |
XCV | 146 |
XCVI | 147 |
XCVII | 149 |
XCVIII | 151 |
XCIX | 153 |
C | 155 |
CI | 158 |
CII | 161 |
CIII | 163 |
CV | 164 |
CVI | 166 |
CVII | 167 |
CVIII | 169 |
CIX | 171 |
CX | 173 |
CXI | 175 |
CXII | 178 |
CXIII | 180 |
CXIV | 183 |
CXV | 185 |
CXVI | 187 |
CXVII | 189 |
CXVIII | 190 |
CXIX | 192 |
CXX | 193 |
CXXI | 196 |
CXXII | 199 |
CXXIII | 202 |
CXXIV | 204 |
CXXV | 207 |
CXXVI | 209 |
CXXVII | 211 |
CXXVIII | 215 |
CXXIX | 216 |
CXXX | 217 |
CXXXI | 220 |
CXXXII | 222 |
CXXXIII | 224 |
CXXXIV | 226 |
CXXXV | 229 |
CXXXVII | 231 |
CXLII | 232 |
| 233 | |
CXLVII | 234 |
CXLIX | 235 |
CLI | 236 |
CLIII | 237 |
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Common terms and phrases
Abelian group algebraic topology axioms based CW complexes based map based spaces basepoint bijection boundary canonical cellular chains chain complex characteristic classes cobordism cochain coefficients cofibration colimits commutative diagram compactly composite construction COROLLARY cover cup product CW complex define definition diagram commutes excisive triad fiber fibration finite following diagram functor fundamental group give given groupoids H-space Hn(M homology and cohomology homology theory homomorphism homotopy classes homotopy equivalence homotopy groups Hurewicz implies inclusion induces an isomorphism integer K-theory LEMMA line bundle long exact sequence manifold map f map g Mayer-Vietoris sequence morphism n-manifold n-plane bundle natural isomorphism natural transformation nondegenerately based obtain oriented path connected Poincaré duality prespectrum PROOF prove q-cells quotient map R-module R-orientation reduced homology restricts result simplicial specified Stiefel-Whitney numbers subcomplex subgroup subset suspension theorem Thom trivial unique vector bundles weak equivalence X₁ zero π₁

