## The Relation of Cobordism to K-theories |

### From inside the book

Results 1-3 of 49

Page 51

Sp By the induction hypotheses , 1 * is an epimorphism ,

Sp By the induction hypotheses , 1 * is an epimorphism ,

**hence**we get a commutative diagram ã * T * i * * 0 Sp ( sent , » n'p ( HP ( n + 1 ) ) * ( HP ( n ) ) = 0 Sp Vez \ t . Juz * * 0 → Ť * ( s4n + 4 ) H * ( HP ( n + 1 ) ) i * → H TM ...Page 66

commutes ,

commutes ,

**hence hence**B ' has Hcl B'en Using the -8n U isomorphism 12 0 C 22 the element [ Mon , e nu corresponding to U B'S has Todd genus T [ Mon , = + 1 according to ( 6.5 ) . It is then sufficient to switch to bordism .Page 104

**Hence**td [ mok + 4 ) is = 0 [ 12 ] , we have the diagram even . SU Since 22 SU = 0 and a 8k + 3 8k + 5 SU ... ( 16.4 ) that ( 1/2 ) Td maps image u into Z.**Hence**we get an induced homomorphism E SU fr : Q - > Q / Z 8k + 3 of Adams [ 3 ] .### 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