## The Relation of Cobordism to K-theories |

### From inside the book

Results 1-3 of 15

Page 34

A standard splitting argument shows that r ( 5 ) u ( 5 ) for all F if it is true for universal line bundles . over

A standard splitting argument shows that r ( 5 ) u ( 5 ) for all F if it is true for universal line bundles . over

**CP**(**n**) . by ( 4.3 ) . Hence ) = 1 and n + 1 ) = 1 Consider then the Hopf complex line bundle S We have M ( Sn ) = CP ...Page 48

(

(

**CP**(**n**) ) such that ( a ) h * (**CP**(**n**) ) is a free h - module with basis tmel Ym ) 2 , ... , 109 ) " , ( b ) inclusion i :**CP**(**n**) CCP ( n + 1 ) has 1 * o nul o n Then there exists a unique function assigning to each U ( m ) ...Page 80

Note that 1 T ” (

Note that 1 T ” (

**CP**(**n**) ) ( t / 11 - e - ty , n + 1 where t is the appropriate generator of HP (**CP**(**n**) ) . We assume the fact ( see Hirzebruch ( 16 ) ) that the coefficient of th in the above is one , and thus that Td (**CP**(**n**) ...### 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