## The Relation of Cobordism to K-theories |

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Page 51

Sp By the induction hypotheses , 1 * is an epimorphism , hence we get a commutative

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 57

Consider the

Consider the

**diagram**KO ( X ) PO ( X ) Sp = dst Ko4 ( 54 1 x ) Els ñ 4 ( 54 ^ X ) Sp མ P1 KSP ( 54 1 x ) and define P. : K ( x ) → Ap ( x ) , for X a finite complex with base point , by ter • P , ༔ - * ༦༩ ) .Page 67

Consider the

Consider the

**diagram**8n ( san , f * ã o SU Now SU ã on ģen ( x ) su va pl SUM KO ( sn ) KO ( 1 ) Po P. ( sån ) ã ( x ) . SU Suppose that f * : Õ * ( son , ( søn , → ñ * ( X ) is non - trivial .### 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