## Algebraic topology: a first course |

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### Contents

SOME OLD TOPOLOGICAL PROBLEMS | 1 |

THE GEOMETRY OF COMPLEXES | 25 |

THE CLASSIFICATION OF SURFACES | 55 |

Copyright | |

10 other sections not shown

### Common terms and phrases

abstract simplicial complex algebraic topology arbitrary assume Betti numbers bordered surfaces boundary Brou Brouwer called cell complex chain maps Claim clearly coefficients compute connected sum constant map continuous map corollary curve DEFINITION deg f denote dimension disk edges equation Euler characteristic Euler's theorem example fact FIGURE finite fixed points follows function geometric given group G homeomorphic homology groups homology theory imbedded induction inessential integer intuitive isomorphism K,cp knot labeled complex labeled polygon Lemma Let f manifolds map f Math n-dimensional n-simplices nonzero orientable surface oriented q-simplex pair path Poin Poincare polyhedra polyhedron Problem proof of Lemma proof of Theorem proved pseudomanifold q q q q-th simplex simplicial approximation simplicial complex simplicial map sphere st(v subcomplex subgroup subset Suppose symbol Theorem 15 topological invariance torsion coefficients torus triangulation Uber underlying space unique vector field vertex vertices zero