## The Relation of Cobordism to K-theories |

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INTRODUCTION These lectures treat certain topics relating

INTRODUCTION These lectures treat certain topics relating

**K**-**theory**and cobordism . Since new connections are in the process of being discovered by various workers , we make no attempt to be definitive but simply cover a few of our ...Page

5 Chapter I. The Thom Isomorphism in

5 Chapter I. The Thom Isomorphism in

**K**-**theory**1. Exterior Algebra ... 2. Tensor products of exterior algebras 3. Application to bundles ....... 4. Thom classes of line bundles 5. Cobordism and homomorphisms into**K**-**theory**The ...Page 52

Characteristic classes in

Characteristic classes in

**K**-**theory**. SU * There was defined in section 5 a homomorphism M : 2 * , ( . ) → Ko * ( . ) ; we also denote the composition 0p ( ) → ( ) * KO * . ) by fa : ( . ) → Ko * ( . ) .### 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