## The Relation of Cobordism to K-theories |

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**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 1

**CHAPTER**I. THE THOM ISOMORPHISM IN K - THEORY . . Given a U ( n ) -bundle 3 over a finite CW complex X there is constructed an element TIE ) E ñ ( M ( 5 ) ) where M ( 5 ) is the Thom space of E ; we call J ( 5 ) the Thom class of G ...Page 69

**CHAPTER**III . U - MANIFOLDS WITH FRAMED BOUNDARIES In this**chapter**we shift from our very general point of view of the previous**chapters**to some very concrete problems on the relationship between U - bordism and K - theory .### 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 | |

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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