## The Relation of Cobordism to K-theories |

### From inside the book

Results 1-3 of 24

Page 36

U U 7 may f : k

U U 7 may f : k

**Suppose**now that M2n is a closed differentiable submanifold of s2n + 2k , with normal bundle Y.**Suppose**also that ~ has a given reduction of structural group to U ( k ) . The cell bundle N associated with be identified ...Page 67

Hence we may

Hence we may

**suppose**[ Wk ] = [ v8m ] ( 51 ) or [ Wk ] = [ v8m ] [ 52 ] [ 51 ] . Then [ mn ] [ vøm , represents 0 in ImI2 SU / Im O. Since this is a polynomial algebra , then [ v8m ) represents zero in Im 2U / Im Əand [ wk ] The lemma ...Page 87

**Suppose**that - Z is a homomorphism . 2n Then 9 can be expressed as an integral linear combination of the homomorphisms ou En . - Z , 11 + * + * + ik $ 11 , ... , n . 2n Proof . Given a partition w = { 11 Ilq 2 .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

CONTENTS 1 | 1 |

Tensor products of exterior algebras | 5 |

Application to bundles | 11 |

Copyright | |

16 other sections not shown

### Other editions - View all

### 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