## The Relation of Cobordism to K-theories |

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Similarly if n = 4k we get a map 9 : Rod ( 5 ) → Rev ( ' ) which above D ( 5 ) X is a real bundle

Similarly if n = 4k we get a map 9 : Rod ( 5 ) → Rev ( ' ) which above D ( 5 ) X is a real bundle

**equivalence**. 2m 2n We can also restate ( 3.1 ) . For we can identify D x D with p2m + 2n , D 5 ) DI thus [ ( 5xp , with D ( 5 ) * DIY ) ...Page 15

This is checked to be an

This is checked to be an

**equivalence**relation . Denote by d ( 56,519 ) the**equivalence**class containing ( 5.51 519 ) g ) and by K ( X , A ) , KU ( X , A ) , KSP ( X , A ) the set of**equivalence**classes . A unique operation is defined on ...Page 78

The stable tangent bundle T + ( 2k - n ) is then a complex vector space bundle , unique up to

The stable tangent bundle T + ( 2k - n ) is then a complex vector space bundle , unique up to

**equivalence**. Denote byli = ' ( M ) K ( M " , the element represented by this complex bundle . Then let T ( M " ) TIT ' ) , T- ( M " , [ T ( ...### 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