## The Relation of Cobordism to K-theories |

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... B ) → K ( X * Y , A * YUX B ) , K ( X / A ) ® X ( Y / B ) → ř { { X / A ) ^ ( Y / B ) ) . over Y. Let 5 denote a

... B ) → K ( X * Y , A * YUX B ) , K ( X / A ) ® X ( Y / B ) → ř { { X / A ) ^ ( Y / B ) ) . over Y. Let 5 denote a

**U**( m ) -**bundle**over a space X and 7 a**U**(**n**) -**bundle**Then we identify M ( 5 XY ) with M ( 5 ) ^ Ml p ) The product ...Page 30

The homomorphism ľco After discussing the cohomology of MU (

The homomorphism ľco After discussing the cohomology of MU (

**n**) and the * classical Thom isomorphism theorem , we go on ... Let E ( 5 ) be the**bundle**space of a right principal**U**(**n**) -**bundle**с E over a space X. The associated sphere ...Page 31

**U**(**n**- 1 ) of**U**(**n**) , hence E ( 5 ) /**U**(**n**- 1 ) = BU (**n**- 1 ) . That is , the natural map D : BU (**n**1 ) - → BU (**n**) induced by**U**(**n**- l ) C U (**n**) ( see Borel [ 8 ] ) may be taken to be the sphere**bundle**over BU (**n**) .### 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