## The Relation of Cobordism to K-theories |

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Page 69

Such manifolds have

Such manifolds have

**Chern classes**and Chern numbers , hence also a Todd genus Td [ M ] which is now a rational number . It is proved that if man is a compact ( U , fr ) -manifold , then there exists a closed U - manifold with the same ...Page 71

Now if we take two different representatives of it is not hard to see that we obtain the same

Now if we take two different representatives of it is not hard to see that we obtain the same

**Chern classes**c , ( MN ) and the same orientation for T + ( 2k - n ) . Since R2k - n has a preferred orientation , the tangent bundle 7 thus ...Page 74

First we need the Atiyah classes Tk ( see [ 5 ] ) ; their existence follows easily from ( 7.6 ) ... Of course the are up to sign just the K - theory

First we need the Atiyah classes Tk ( see [ 5 ] ) ; their existence follows easily from ( 7.6 ) ... Of course the are up to sign just the K - theory

**Chern classes**k of Chapter II . Just as for cohomology**Chern classes**, we can form ...### What people are saying - Write a review

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### Contents

CONTENTS 1 | 1 |

Tensor products of exterior algebras | 5 |

Application to bundles | 11 |

Copyright | |

16 other sections not shown

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### Common terms and phrases

abelian According acts Adams assigning associated base point basis bordism bordism classes BSp(n Chapter characteristic Chern classes Chern numbers classes closed U-manifold cobordism coefficient commutativity compact U,fr)-manifold complex vector space composition consider construction COROLLARY CP(n define definition denote diagram dimension element equivalence exact exists fact fiber finite CW complex follows function give given Hence holds homo topy homomorphism HP(n identified induced integer isomorphism K-theory KSP(X line bundle linear manifold Moreover MU(K Namely natural Note obtain particular partition polynomial Proof prove quaternionic represented respectively ring seen Similarly stable tangent bundle stably framed structure su(n sufficient Suppose theorem Thom Todd genus trivial U-structure U,fr U(n)-bundle unique universal vector space bundle