## The Relation of Cobordism to K-theories |

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Page 11

Application to bundles . In this section the constructions of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . For example , given an SU ( 2k ) -bundle § there are associated two real

Application to bundles . In this section the constructions of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . For example , given an SU ( 2k ) -bundle § there are associated two real

**vector space bundles**...Page 12

Replacing Av by 1 odvi , nervi respectively in the above , we obtain bundles od 1 ( 5 ) → X and 1 ( E ) > X. ev If ... If n = 0 mod 4 , we get a real

Replacing Av by 1 odvi , nervi respectively in the above , we obtain bundles od 1 ( 5 ) → X and 1 ( E ) > X. ev If ... If n = 0 mod 4 , we get a real

**vector space bundle**R ( 3 ) → X , where R ( E ) = = { x Alternatively , x : x6115 ) ...Page 13

In the above , given

In the above , given

**vector space bundles**o → X and Y Y we mean by p By → X X Y the**vector space bundle**whose fiber above ( x , y ) is p - ' ( x ) » -f ( y ) . Also in cases 1 and 4 , the two bundles are equivalent as real vector ...### 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