## The Relation of Cobordism to K-theories |

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Page 28

Let Le xe ãn ( X ) be

Let Le xe ãn ( X ) be

**represented**by f : S ^ X- MSU ( 4k ) . Let play be the image of t in the composition s ' KO ( MSU ( 4k ) ) → KO ( 58k - n 1 x ) ~ Kon - 8k ( x ) Kor ( x ) . n ăn SU SU 8k - n 4k We leave it to the reader to verify ...Page 29

... 4 ^ ( MSU ( 45 ) ) toi sok x x 8 → MSU ( 4k + 2 ) 4 where f and g

... 4 ^ ( MSU ( 45 ) ) toi sok x x 8 → MSU ( 4k + 2 ) 4 where f and g

**represent**an element of 2 ( X ) . ... there is a multiplicative trans* * : K ( ) sending the element a E U n و ñ с ulo ) formation R ( X )**represented**by f : saken X ...Page 100

Regard fi • 220 = 0 , there 2n - 1 as

Regard fi • 220 = 0 , there 2n - 1 as

**representing**an element of T ( MU ( k ) ) 2n + 2k - 1 exists an extension of f ' to a map ( D2n + 2 % , 52n + 2k - 1 , → ( MU ( K ) , sek ) , from which , passing to quotients , we get a map ...### 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