## A course in simple-homotopy theory |

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### Contents

Introduction 1 Homotopy equivalence | 1 |

2 Whiteheads combinatorial approach to homotopy theory | 2 |

3 CW complexes | 4 |

Copyright | |

26 other sections not shown

### Common terms and phrases

abelian group acyclic algebraic assume base points boundary operator cellular homotopy equivalence cellular map chain complex chain contraction chain map characteristic map Clearly components covering homeomorphisms CW complexes CW pair define definition deformation retraction denote elementary collapse equivalence classes equivariant fact finite CW complexes follows formal deformation free module functor G)-complex given GL(R group of covering Hence homotopy equivalence implies inclusion map induced map integer J. H. C. Whitehead KG(R lemma lens spaces Let g lift mapping cylinder Milnor morphism natural projection non-singular non-trivial unit orientation p.l. homeomorphic preferred basis PROOF properties prove quotient map reader satisfies short exact sequence simple isomorphism simple-homotopy equivalence simple-homotopy type simplicial complex simplified form stably free strong deformation retraction subcomplex subgroup Suppose t(Kx theory topology trivial complex trivial units universal covering space well-defined Wh(G Wh(L Whitehead group