## The Relation of Cobordism to K-theories |

### From inside the book

Results 1-3 of 49

Page 14

We now digress to

We now digress to

**define**the groups K ( X , A ) , KO ( X , A ) , KSP ( X , A ) , A using a**definition**that builds in Atiyah's difference construction 1P ) where 5 and 5 O 1 ( 7,22 ] . Fix a pair ( X , A ) of finite CW complexes ...Page 91

As with U - structures , given a stable framing e of in one can

As with U - structures , given a stable framing e of in one can

**define**a stable framing e ; one can also**define**a stable framing se on om and thus**define**- ( M " , 0 ) = ( M ” , - ) , a ( m , e ) = ( oi , 00 ) . by fr For more details ...Page 103

In U u fr o → a 220 , fr Qy → 0 , 2n 2n 2n - 1 U It is 2n

In U u fr o → a 220 , fr Qy → 0 , 2n 2n 2n - 1 U It is 2n

**define**DC afr to be the image under o of tor eu , fr 2n - 1 easily verified that LED if and only if given ( menine Q20 , fr with o [ men , = there exists a closed U - manifold ...### 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