## Additive Invariants of Manifolds with Boundary |

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### Contents

The Gohomolopy Ring H | 9 |

U The Characterization of the Index | 14 |

Euler Characteristics | 19 |

2 other sections not shown

### Common terms and phrases

2.1 Proposition 6.U Theorem additive invariant adjunction space algebra bilinear pairing characteristic classes classes of compact closed manifold closed oriented Cobordism Theory cobordlsm cohomology compact manifolds compact oriented manifolds components of dM Conner and Floyd Conner-Floyd Corollary CP(k defined denote diffeomorphism classes dimension disjoint union duality equivariant Euler characteristic even-dimensional exist k(n fiber bundle fixed set free abelian free abelian group free involution given graded abelian group Hence homomorphism implies induces integer isomorphic Lemma Let cr let f manifolds with boundary manifolds with free Manifolds with Involution Math Morse function n-manifold neighborhood nonzero O-bundLs odd prime odd-dimensional orbit space P. E. Conner phism preserves relations Princeton Proof prove RP(n Russell Johnston semigroup under disjoint sequence Stong subsemigroup surgery torsion elements trivial trivial bundle union of components University of Virginia well-defined Z^-vector space zero