## Surgery on simply-connected manifolds |

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### Contents

Poincare Duality | 1 |

The Main Results of Surgery | 30 |

The Invariant ct | 51 |

Copyright | |

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### Common terms and phrases

1-connected Arf invariant base point bilinear form bundle map c-plane bundle cap product chain complex chain map cobordant rel cohomology collapsing map commutative diagram compact Corollary defines a normal diffeomorphism disk Dm+k x Dp+1 Dq+1 duality map element exact sequence fibre homotopy equivalence fibre map geometric chain pair Hence homeomorphism homology homotopy classes homotopy type Hq(B Hq(X inclusion intersection Kq(B Kq(M Kq(X Lemma Let f linear bundle map manifold with boundary map of degree matrix monomorphism morphism natural collapsing non-singular normal bundle normal cobordism relB normal fibre space normal map normal surgery orientation class oriented Poincare orthogonal pair of dimension plumbing Poincare chain pair Poincare duality Poincare pair Proof properties Proposition quadratic form recall regular neighborhood represented S-dual smooth manifold SO(q spherical fibre space Spivak normal fibre subspace summand suppose Thom class Thom complexes total space trivial zero