## Algebraic topology |

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### Contents

Analytic and Algebraic Topology | 1 |

Problems and Examples | 5 |

SIMPLICIAL COMPLEXES Chaper 1 GEOMETRY OF SIMPLICIAL COMPLEXES 3 Hulls and Stars | 15 |

Copyright | |

16 other sections not shown

### Common terms and phrases

8cq+ algebraic arbitrary assertion assigned barystar basic cycle basis elements Betti numbers boundary operator called canonical bases carrier simplex cell decomposition chain complex chain cq chain mapping coboundary cochain cocycle cohomology classes complementary cells completes the proof connected continuous mapping corresponding Cq(K cup product cyclic groups defined definition deformation deformation retract denote dimension q dimensional elementary chain epimorphic equation example finite number following theorem group Hq(R groups and cohomology Hence homo homology theory homomorphism homotopy type Hq(K Hq(S identity mapping induced integer invariant isomorphic Kronecker product manifold Mn mapping f matrix Mobius band modules morphism normal subdivision oriented simplex polyhedra polyhedron pseudomanifold retract simplex simplicial approximation simplicial complex simplicial decomposition simplicial mapping solid sphere space star condition stars St subcomplex summands topological uniquely determined valid vertex stars vertices w-dimensional w-simplexes zero