## The Relation of Cobordism to K-theories |

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Page 71

It may be seen from this that the giving of a U -

It may be seen from this that the giving of a U -

**structure**is independent of the precise value of k at least if 2k - n - 2 ( see ( 12 , p . 16 ] ) . Similarly if E ( ? ) admits such a natural operator J , then mh receives a natural To ...Page 72

1 ; for each U n sketch . on min 2 [ Menj , i It is convenient to have at hand the U - bordism groups 12 We shall not give complete definitions ( see [ 12 ] ) but simply a quick It is possible to associate with each U -

1 ; for each U n sketch . on min 2 [ Menj , i It is convenient to have at hand the U - bordism groups 12 We shall not give complete definitions ( see [ 12 ] ) but simply a quick It is possible to associate with each U -

**structure**0 a ...Page 105

Such a ( U , SU ) -

Such a ( U , SU ) -

**structure**induces a natural SU -**structure**on OBh of Note that the cross - section of U > on induces a principal U ( 1 ) -bundle over B , which along 9 Bh already has a homo topy class of cross - sections ; thus , the ...### 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