## The Relation of Cobordism to K-theories |

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Page 11

In this section the

In this section the

**constructions**of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . ... Using Atiyah's difference**construction**, one obtains an element t ( $ ) E KO ( D ( 5 ) , OD ( 5 ) ) where t ( & ) dl ...Page 37

In the above

In the above

**construction**one simply puts a suitable complex structure on the stable tangent bundle of Man . ( 6.5 ) COROLLARY . The composition Mc -2n au ño ( pt ) → K ( pt ) = 2 ° 2n U maps a cobordism class [ manj of closed weakly ...Page 108

... su ε Ο The purpose of this section is the

... su ε Ο The purpose of this section is the

**construction**of SU those elements in 12 which can be represented by a stably framed 8k + 1 closed manifold . fr ( 18.1 ) LEMMA : Let [ v , be an element of order 2 and let n [ ik ] € ( SU be ...### 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