## The Relation of Cobordism to K-theories |

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If X is a

If X is a

**finite CW complex**with base point x , then the map { x } → X induces K ( X ) → Kl { x } ) ; it is customary to denote the kernel by K ( X ) . There is a homomorphism K ( x , x ) = ( x ) sending 015657P ) into 5 - 5 : We ...Page 39

as in section 4 , defined on the category of

as in section 4 , defined on the category of

**finite CW complexes**with base point . As is well - known , there is generated a multiplicative cohomology theory h ( • ) on the category of finite CW pairs . For a finite cw pair ( X , A ) ...Page 40

satisfies the Eilenberg - Steenrod axioms except for the dimensional axiom . There is also a cup product h ( X , A ) n ( x , B ) → h ( x , A UB ) sending a binto a b . ( 7.1 ) Let X be a

satisfies the Eilenberg - Steenrod axioms except for the dimensional axiom . There is also a cup product h ( X , A ) n ( x , B ) → h ( x , A UB ) sending a binto a b . ( 7.1 ) Let X be a

**finite cw complex**and let yn denote its n ...### 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