## The Relation of Cobordism to K-theories |

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Page 53

It follows by induction on k that ko * ( sk ) is a free ko * -module with a basis consisting of one element u of kok ( sk ) ,

It follows by induction on k that ko * ( sk ) is a free ko * -module with a basis consisting of one element u of kok ( sk ) ,

**namely**any element with ph 3 the image of a generator under ( sk ; z ) ▻ yk ( sk ; Q ) .Page 54

4 ( 7 )

4 ( 7 )

**Namely**, Ko4 ( x ) = ko ( s4 - X ) and given y E K $ p ( x ) we let ( 1 - 5 3 ) Quy where 5 , is the Hopf Sp ( 1 ) -bundle over 84 . It follows from the above paragraph that ph O ( n ) = chy : ( 9.1 ) The ko * -module ko * ( HP ...Page 78

... given as follows :

... given as follows :

**namely**in ( 1 - ero , ... ( 1 - ( n , ti ••• tn replace Et , by cz ( 3 ) , " ' , Et ; " " tk byc by ck ( 5 ) , • * . 13 . Characteristic numbers from K - theory . 2n Assume that we are given a compact U - manifold ...### 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