## The Relation of Cobordism to K-theories |

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Page 66

First we According have to convert the statement to one in terms of

First we According have to convert the statement to one in terms of

**bordism**. to section 5 , 2. ( . ) SU x1 on -8n E no + 1 . U -on > on on on SU the KO ^ ( . ) ov Кс ೧೫- ) Ko ( . ) commutes , hence hence B ' has Hcl B'en Using the ...Page 69

U - MANIFOLDS WITH FRAMED BOUNDARIES In this chapter we shift from our very general point of view of the previous chapters to some very concrete problems on the relationship between U -

U - MANIFOLDS WITH FRAMED BOUNDARIES In this chapter we shift from our very general point of view of the previous chapters to some very concrete problems on the relationship between U -

**bordism**and K - theory . In section 12 we consider ...Page 72

1 ; for each U n sketch . on min 2 [ Menj , i It is convenient to have at hand the U -

1 ; for each U n sketch . on min 2 [ Menj , i It is convenient to have at hand the U -

**bordism**groups 12 We shall not give complete definitions ( see [ 12 ] ) but simply a quick It is possible to associate with each U - structure 0 a ...### 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