## Algebraic Topology: A First CourseGreat first book on algebraic topology. Introduces (co)homology through singular theory. |

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### Contents

3 | |

6 | |

11 | |

16 | |

21 | |

26 | |

32 | |

Singular Homology Theory | 37 |

Spherical Complexes | 112 |

Betti Numbers and Enter Characteristic | 128 |

Cell Complexes and More Adjunction Spaces | 134 |

Orientation and Duality on Manifolds | 153 |

Introduction to Part ID | 155 |

Orientation of Manifolds | 157 |

Singular Cohomology | 174 |

Cup and Cap Products | 195 |

Introduction to Part II | 39 |

Affine Preliminaries | 41 |

Singular Theory | 44 |

Oiain Complexes | 52 |

Homotopy Invariance of Homology | 59 |

Relation Between and H | 63 |

Relative Homology | 70 |

The Exact Homology Sequence | 75 |

The Excision Theorem | 82 |

Further Applications to Spheres | 94 |

MayerVietoris Sequence | 98 |

The JordanBrouwer Separation Theorem | 106 |

Algebraic limits | 208 |

Poincare Duality | 215 |

Alexander Duality | 230 |

Lefechetz Duality | 237 |

PartrV Products and Lefscbetz Fixed Point Theorem | 247 |

Introduction to Part IV | 249 |

Products | 251 |

Thorn Class and Leftehetz Fixed Point Theorem | 276 |

Intersection Numbers and Cup Products | 290 |

Table of Symbols | 301 |

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### Common terms and phrases

algebraic topology augmentation calculate called canonical chain complex chain equivalence chain homotopy chain map closed coboundary cochain coefficients cohomology commutative diagram components consider construct coordinate neighborhood Corollary covering space cup product define definition deformation retract denote dimension direct sum disjoint union duality theorems element Example excision Exercise finite fixed point follows formula functor fundamental group given Hence homology class homology modules homology theory homotopy equivalence homotopy groups Hq(X identify inclusion induces an isomorphism integer intersection invariant inverse kernel Lemma linear loop manifold mapping cone Mayer-Vietoris sequence morphism Note obtain open neighborhood open sets orientation pair path Poincare duality projective Proof properties Proposition prove quotient space R-orientation Remark resp short exact sequence Show simply connected singular simplex spherical complex Sq(X subgroup Sublemma submodule subset subspace Suppose torus unique vector field Z/pZ zero

### Popular passages

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