## The Relation of Cobordism to K-theories |

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For example , given an SU ( 2k ) -bundle § there are

For example , given an SU ( 2k ) -bundle § there are

**associated**two real vector space bundles Rod ( 5 ' ) and Rev ( 5 ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle**associated**with 5 with fiber the unit ball D ...Page 30

Let E ( 5 ) be the bundle space of a right principal U ( n ) -bundle с E over a space X. The

Let E ( 5 ) be the bundle space of a right principal U ( n ) -bundle с E over a space X. The

**associated**sphere bundle is given by E ( 5 ) x ( U ( n ) / U ( n - 1 ) ) / U ( n ) → X. There is an identification E ( 5 ) x ( U ( n ) / U ( n ...Page 98

2ntük Then < ch tlk ) * Td [ men , qk ) 0 * f * ( 0 ) > . Proof . If man is a closed U - manifold with

2ntük Then < ch tlk ) * Td [ men , qk ) 0 * f * ( 0 ) > . Proof . If man is a closed U - manifold with

**associated**map & : s2n + 2K - MU ( K ) , it may be verified that T [ Man , ích T ( k ) +84 98.### 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