## The Relation of Cobordism to K-theories |

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Page 12

Replacing Av by 1 odvi , nervi

Replacing Av by 1 odvi , nervi

**respectively**in the above , we obtain bundles od 1 ( 5 ) → X and 1 ( E ) > X. ev If n = 2 mod 4 then je defines a quaternionic bundle structure on 1 ( 3 ) , so that in this case we consider 115 ) → X a ...Page 48

+ 6015 ) ૬ ) where ( 5 ) E hæk ( X ) , such that k ( 1 ) a bundle map f : 5 → y covering a map † : X → Y of base spaces has 7 * 617 ) = c ( 5 ) , ( 2 ) if 5 , » are u ( m ) , U ( n ) -hundles over x

+ 6015 ) ૬ ) where ( 5 ) E hæk ( X ) , such that k ( 1 ) a bundle map f : 5 → y covering a map † : X → Y of base spaces has 7 * 617 ) = c ( 5 ) , ( 2 ) if 5 , » are u ( m ) , U ( n ) -hundles over x

**respectively**then in c ( 5 Rp ) ...Page 105

Let U → B " and SU → on

Let U → B " and SU → on

**respectively**denote the associated bundle with fibre 0 ( 2m ) / U ( m ) and 0 ( 2m ) / SU ( m ) . There is the principal fibring 8U - > U with fibre U ( m ) / SU ( m ) U ( 1 ) .### 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